NameCaraballo Garrido, Tomás
DepartmentEcuaciones Diferenciales y Análisis Numérico
Knowledge areaAnálisis Matemático
Professional categoryCatedrático de Universidad
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Invariant measures for stochastic 3D Lagrangian-averaged Navier–Stokes equations with infinite delayInvariant measures for stochastic 3D Lagrangian-averaged Navier–Stokes equations with infinite delay

Yang, Shuang; Yang, Shuang; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Li, Yangrong; Li, Yangrong (Elsevier, 2023-04-05)
In this paper we investigate stochastic dynamics and invariant measures for stochastic 3D Lagrangian-averaged NavierStokes ...
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Dynamics of Nonautomous Impulsive Multivalued ProcessesDynamics of Nonautomous Impulsive Multivalued Processes

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Uzal, José M.; Uzal, José M. (Springer, 2023-02-10)
In this paper we study the asymptotic behaviour of multivalued processes which are under the influence of impulsive action. ...
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Lyapunov functionals and practical stability for stochastic differential delay equations with general decay rateLyapunov functionals and practical stability for stochastic differential delay equations with general decay rate

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ezzine, Faten; Ezzine, Faten; Hammami, Mohamed Ali; Hammami, Mohamed Ali (Bolyai Institute, University of Szeged, 2022-12-01)
This paper stands for the almost sure practical stability of nonlinear stochastic differential delay equations (SDDEs) ...
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NONTRIVIAL EQUILIBRIUM SOLUTIONS AND GENERAL 2 STABILITY FOR STOCHASTIC EVOLUTION EQUATIONS WITH PANTOGRAPH DELAY AND TEMPERED FRACTIONAL NOISE∗NONTRIVIAL EQUILIBRIUM SOLUTIONS AND GENERAL 2 STABILITY FOR STOCHASTIC EVOLUTION EQUATIONS WITH PANTOGRAPH DELAY AND TEMPERED FRACTIONAL NOISE∗

Liu, Yarong; Liu, Yarong; Wang, Yejuan; Wang, Yejuan; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (SIAM, 2022-10-07)
In this paper, we study the full compressible Navier--Stokes system in a bounded domain Ω⊂R3 , where the viscosity and ...
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Random attractors for stochastic delay wave equations on Rn with linear memory nad nonlinear dampingRandom attractors for stochastic delay wave equations on Rn with linear memory nad nonlinear damping

Wang, Jingyu; Wang, Jingyu; Wang, Yejuan; Wang, Yejuan; Yang, Lin; Yang, Lin; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (AIMS, 2022-10-01)
A non-autonomous stochastic delay wave equation with linear memory and nonlinear damping driven by additive white noise ...
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Asymptotic behavior of nonlocal partial differential equations with long time memoryAsymptotic behavior of nonlocal partial differential equations with long time memory

Xu, Jiaohui; Xu, Jiaohui; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Valero, José; Valero, José (AIMS, 2022-10-01)
In this paper, it is first addressed the well-posedness of weak solutions to a nonlocal partial differential equation with ...
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Multi-valued random dynamics og stochastic wave equations with infinite delaysMulti-valued random dynamics og stochastic wave equations with infinite delays

Wang, Jingyu; Wang, Jingyu; Wang, Yejuan; Wang, Yejuan; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (AIMS, 2022-10-01)
This paper is devoted to the asymptotic behavior of solutions to a non-autonomous stochastic wave equation with infinite ...
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Dynamics of a globally modified Navier–Stokes model with double delayDynamics of a globally modified Navier–Stokes model with double delay

Yang, Dandan; Yang, Dandan; Chen, Zhang; Chen, Zhang; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Springer, 2022-09-27)
This paper investigates the dynamics of a class of three-dimensional globally modified Navier-Stokes equations with double ...
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Mean square stability for controlled hybrid neutral stochastic differential equations with in nite delayMean square stability for controlled hybrid neutral stochastic differential equations with in nite delay

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Mchiri, Lassaad; Mchiri, Lassaad; Mohsen, Belfeki; Mohsen, Belfeki; Rhaima, Mohamed; Rhaima, Mohamed (Wiley, 2022-09-27)
In this article, we investigate the existence and uniqueness of solution of controlled hybrid neutral stochastic di erential ...
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Dynamical stability of random delayed FitzHugh-Nagumo lattice systems driven by nonlinear Wong-Zakai noiseDynamical stability of random delayed FitzHugh-Nagumo lattice systems driven by nonlinear Wong-Zakai noise

Yang, Shuang; Yang, Shuang; Li, Yangrong; Li, Yangrong; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (AIP Publishing, 2022-09-11)
In this paper, two problems related to FitzHugh-Nagumo lattice systems are analyzed. The first one is concerned with the ...
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A new result on stabilization analysis for stochastic nonlinear affine systems via Gamidov’s inequalityA new result on stabilization analysis for stochastic nonlinear affine systems via Gamidov’s inequality

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ezzine, Faten; Ezzine, Faten; Hammami, Mohamed Ali; Hammami, Mohamed Ali (Springer, 2022-09-01)
The Lyapunov approach is one of the most effective and efficient methods for the inves tigation of the stability of ...
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Asymptotic behavior of a semilinear problem in heat conduction with long time memory and non-local diffusionAsymptotic behavior of a semilinear problem in heat conduction with long time memory and non-local diffusion

Xu, Jiaohui; Xu, Jiaohui; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Valero, José; Valero, José (Elsevier, 2022-08-01)
In this paper, the asymptotic behavior of a semilinear heat equation with long time memory and non-local diffusion is ...
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A 3D isothermal model for nematic liquid crystals 1 with delay termsA 3D isothermal model for nematic liquid crystals 1 with delay terms

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Cavaterra, Cecilia; Cavaterra, Cecilia (2022-08-01)
In this paper we consider a model describing the evolution of a nematic liquid crystal flow with delay external forces. ...
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WELL-POSEDNESS OF STOCHASTIC TIME FRACTIONAL 2D-STOKES MODELS WITH FINITE AND INFINITE DELAYWELL-POSEDNESS OF STOCHASTIC TIME FRACTIONAL 2D-STOKES MODELS WITH FINITE AND INFINITE DELAY

Xu, Jiaohui; Xu, Jiaohui; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Texas State University, 2022-06-19)
We analyze the well-posedness of two versions of a stochastic time delay fractional 2D-Stokes model with nonlinear ...
Master's Final Project
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Dinámica de un Quimiostato no autónomo con retardoDinámica de un Quimiostato no autónomo con retardo

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; López de la Cruz, Javier; López de la Cruz, Javier (2022-06-15)
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η-stability of hybrid neutral stochastic differential equations with infinite delayη-stability of hybrid neutral stochastic differential equations with infinite delay

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Mchiri, Lassaad; Mchiri, Lassaad; Mohsen, Belfeki; Mohsen, Belfeki (Wiley, 2022-03-01)
In this paper, we study the η-stability in q-th moment (η.s.q.m) of hybrid neutral stochastic differential equations with ...
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Partial asymptotic stability of neutral pantograph stochastic differential equations with Markovian switchingPartial asymptotic stability of neutral pantograph stochastic differential equations with Markovian switching

Mchiri, Lassaad; Mchiri, Lassaad; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Rhaima, Mohamed; Rhaima, Mohamed (Springer, 2022-02-25)
In this paper, we investigate the partial asymptotic stability (PAS) of neutral pantograph stochastic differential equations ...
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New criteria for global asymptotic stability of linear neutral differential equations by a fixed point approachNew criteria for global asymptotic stability of linear neutral differential equations by a fixed point approach

; ; Benhadri, Mimia; Benhadri, Mimia; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Scopus, 2022-02-22)
New criteria ensuring global asymptotic stability of the zero solution for a class of linear neutral differential equations ...
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Invariant sample measures and random Liouville type theorem for the two-dimensional stochastic Navier-Stokes equationsInvariant sample measures and random Liouville type theorem for the two-dimensional stochastic Navier-Stokes equations

Zhao, Caidi; Zhao, Caidi; Wang, Jintao; Wang, Jintao; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Elsevier, 2022-02-17)
In this article, we first prove some sufficient conditions guaranteeing the existence of invariant sample measures for ...
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Ulam-Hyers-Rassias stability of neutral stochastic functional differential equationsUlam-Hyers-Rassias stability of neutral stochastic functional differential equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Mchiri, Lassaad; Mchiri, Lassaad; Rhaima, Mohamed; Rhaima, Mohamed (Taylor & Francis, 2022-02-01)
In this paper, by using the Gronwall inequality, we show two new results on the UlamHyers and the Ulam-Hyers-Rassias stabilities of neutral stochastic functional differential equations. Two examples illustrating our results are exhibited.
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Smoothing effect and asymptotic dynamics of nonautonomous parabolic equations with time-dependent linear operatorsSmoothing effect and asymptotic dynamics of nonautonomous parabolic equations with time-dependent linear operators

Boldrin Belluzi, Maykel; Boldrin Belluzi, Maykel; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Nascimento, Marcelo J.D.; Nascimento, Marcelo J.D.; Schiabel, Karina; Schiabel, Karina (Elsevier, 2022-01-24)
In this paper we consider the nonautonomous semilinear parabolic problems with time-dependent linear operators ut + A(t)u ...
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On a terminal value problem for parabolic reaction–diffusion systems with nonlocal coupled diffusivity termsOn a terminal value problem for parabolic reaction–diffusion systems with nonlocal coupled diffusivity terms

NGuyen, Huy Tuan; NGuyen, Huy Tuan; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Khanh Van, Phan Thi; Khanh Van, Phan Thi; Van Au, Vo; Van Au, Vo (Elsevier, 2022-01-10)
In this article, we are interested in investigating the nonlocal nonlinear reaction– diffusion system with final conditions. ...
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Long Time Behavior of Stochastic Nonlocal Partial Differential Equations and Wong--Zakai ApproximationsLong Time Behavior of Stochastic Nonlocal Partial Differential Equations and Wong--Zakai Approximations

Xu, Jiaohui; Xu, Jiaohui; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (SIAM, 2022-01-01)
This paper is devoted to investigating the well-posedness and asymptotic behavior of a class of stochastic 5 nonlocal ...
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Strong solutions for semilinear problems with almost sectorial operatorsStrong solutions for semilinear problems with almost sectorial operators

Boldrin Belluzi, Maykel; Boldrin Belluzi, Maykel; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Nascimento, Marcelo J.D.; Nascimento, Marcelo J.D.; Schiabel, Karina; Schiabel, Karina (Springer, 2022-01-01)
In this paper we study a semilinear parabolic problem ut + Au = f(t, u), t > τ ; u(τ ) = u0 ∈ X, in a Banach space X, where ...
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On the existence of positive periodic solutions for n−species Lotka-Volterra competitive systems with distributed delays and impulsesOn the existence of positive periodic solutions for n−species Lotka-Volterra competitive systems with distributed delays and impulses

Benhadri, Mimia; Benhadri, Mimia; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Springer, 2021-11-11)
In this paper, we investigate the existence of positive periodic solutions for an n-species Lotka-Volterra system with ...
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p-th moment exponential stability of neutral stochastic pantograph differential equations with Markovian switchingp-th moment exponential stability of neutral stochastic pantograph differential equations with Markovian switching

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Mchiri, Lassaad; Mchiri, Lassaad; Mohsen, Belfeki; Mohsen, Belfeki; Rhaima, Mohamed; Rhaima, Mohamed (Elsevier, 2021-11-01)
In this paper we focus on the p-th moment exponential stability of neutral stochastic pantograph differential equations ...
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h-stability in p-th moment of neutral pantograph stochastic di erential equations with Markovian switching driven by L evy noiseh-stability in p-th moment of neutral pantograph stochastic di erential equations with Markovian switching driven by L evy noise

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Belfeki, Mohsen; Belfeki, Mohsen; Mchiri, Lassaad; Mchiri, Lassaad; Rhaima, Mohamed; Rhaima, Mohamed (Elsevier, 2021-10-01)
In this paper we investigate the h-stability in p-th moment of neutral pantograph stochastic differential equations with ...
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Analysis of a stochastic coronavirus (COVID-19) L´evy jump model with protective measuresAnalysis of a stochastic coronavirus (COVID-19) L´evy jump model with protective measures

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; El Fatini, Mohamed; El Fatini, Mohamed; El Khalifi, Mohamed; El Khalifi, Mohamed; Rathinasamy, Anandaraman; Rathinasamy, Anandaraman (Taylor & Francis, 2021-09-30)
This paper studied a stochastic epidemic model of the spread of the novel coronavirus (COVID19). Severe factors impacting ...
PhD Thesis
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Singularly nonautonomous semilinear evolution equations with almost sectorial operatorsSingularly nonautonomous semilinear evolution equations with almost sectorial operators

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Schiabel, Karina; Schiabel, Karina; Boldrin Belluzi, Maykel; Boldrin Belluzi, Maykel (2021-09-21)
In this work we consider the singularly nonautonomous semilinear parabolic problem ut + A(t)u = F(u); t > ; u( ) = u0; in ...
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The continuity, regularity and polynomial stability of mild solutions for stochastic 2D-Stokes equations with unbounded delay driven by tempered fractional Gaussian noiseThe continuity, regularity and polynomial stability of mild solutions for stochastic 2D-Stokes equations with unbounded delay driven by tempered fractional Gaussian noise

Liu, Yarong; Liu, Yarong; Wang, Yejuan; Wang, Yejuan; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (World scientific, 2021-09-01)
We consider stochastic 2D-Stokes equations with unbounded delay in fractional power spaces and moments of order p ≥ 2 ...
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Study of the dynamics of two chemostats connected by Fickian diffusion with bounded random fluctuationsStudy of the dynamics of two chemostats connected by Fickian diffusion with bounded random fluctuations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; López de la Cruz, Javier; López de la Cruz, Javier; Rapaport, Alain; Rapaport, Alain (World scientific, 2021-09-01)
This paper investigates the dynamics of a model of two chemostats connected by Fickian diffusion with bounded random ...
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New sufficient conditions for global asymptotic stability of a kind of nonlinear neutral differential equationsNew sufficient conditions for global asymptotic stability of a kind of nonlinear neutral differential equations

Benhadri, Mimia; Benhadri, Mimia; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (DOAJ, 2021-09-01)
This paper addresses the stability study for nonlinear neutral differ ential equations. Thanks to a new technique based ...
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Partial stability analysis of stochastic differential equations with a general decay ratePartial stability analysis of stochastic differential equations with a general decay rate

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ezzine, Faten; Ezzine, Faten; Hammami, Mohamed Ali; Hammami, Mohamed Ali (Springer, 2021-08-28)
This paper is concerned with the almost sure partial practical stability of stochastic differential equations with general ...
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Dynamics of stochastic nonlocal partial differential equationsDynamics of stochastic nonlocal partial differential equations

Xu, Jiaohui; Xu, Jiaohui; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Springer, 2021-08-17)
This paper is concerned with the asymptotic behavior of solutions to nonlocal stochastic partial differential equations ...
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Strong solution for singularly nonautonomous evolution equation with almost sectorial operatorsStrong solution for singularly nonautonomous evolution equation with almost sectorial operators

Boldrin Belluzi, Maykel; Boldrin Belluzi, Maykel; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Dias Nascimento, Marcelo José; Dias Nascimento, Marcelo José; Schiabel, Karina; Schiabel, Karina (American Institute of Mathematical Sciences, 2021-08-04)
ct. In this paper we consider the singularly nonautonomous evolution problem ut + A(t)u = f(t), τ < t < τ + T; u(τ) = u0 ...
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On the initial value problem for a class of nonlinear biharmonic equation with time-fractional derivativeOn the initial value problem for a class of nonlinear biharmonic equation with time-fractional derivative

Tuan Nguyen, Anh; Tuan Nguyen, Anh; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Tuan, Nguyen Huy; Tuan, Nguyen Huy (Elsevier, 2021-08-01)
In this work, we investigate the IVP for a time-fractional fourth-order equation with nonlinear source terms. More ...
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On a nonlinear volterra integrodifferential equation involving fractional derivative with Mittag-Leffler KernelOn a nonlinear volterra integrodifferential equation involving fractional derivative with Mittag-Leffler Kernel

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ngoc, Tran Bao; Ngoc, Tran Bao; Tuan, Nguyen Huy; Tuan, Nguyen Huy; Wang, Renhai; Wang, Renhai (American Mathematical Society, 2021-08-01)
In this paper, a nonlinear time-fractional Volterra equation with nonsingular Mittag-Leffler kernel in Hilbert spaces is ...
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On stochastic nonclassical diffusion equation with standard and fractional Brownian motionOn stochastic nonclassical diffusion equation with standard and fractional Brownian motion

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ngoc, Tran Bao; Ngoc, Tran Bao; Thach, Tran Ngoc; Thach, Tran Ngoc; Tuan, Nguyen Huy; Tuan, Nguyen Huy (World scientific, 2021-07-15)
This paper is concerned with the mathematical analysis of terminal value problems for a stochastic non-classical diffusion ...
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New stability criteria for stochastic perturbed singular systems in mean squareNew stability criteria for stochastic perturbed singular systems in mean square

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ezzine, Faten; Ezzine, Faten; Hammami, Mohamed Ali; Hammami, Mohamed Ali (Springer, 2021-06-24)
In this paper, we investigate the problem of stability of time-varying stochastic perturbed singular systems by using ...
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On terminal value problems for bi-parabolic equations driven by Wiener process and fractional Brownian motionsOn terminal value problems for bi-parabolic equations driven by Wiener process and fractional Brownian motions

NGuyen, Huy Tuan; NGuyen, Huy Tuan; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Tran, Ngoc Thach; Tran, Ngoc Thach (IOS Press, 2021-06-09)
In this paper, we study two terminal value problems (TVPs) for stochastic bi-parabolic equations perturbed by standard ...
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Partial practical exponential stability of neutral stochastic functional di erential equa- tions with Markovian switchingPartial practical exponential stability of neutral stochastic functional di erential equa- tions with Markovian switching

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Mchiri, Lassaad; Mchiri, Lassaad; Rhaima, Mohamed; Rhaima, Mohamed (Springer, 2021-06-03)
In this paper, we investigate the partial practical exponential stability of neutral stochastic functional differential ...
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Corrigendum to the paper: A way to model stochastic perturbations in population dynamics models with bounded realizations. Commun Nonlinear Sci Numer Simulat, 77 (2019), 239–257Corrigendum to the paper: A way to model stochastic perturbations in population dynamics models with bounded realizations. Commun Nonlinear Sci Numer Simulat, 77 (2019), 239–257

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato; López de la Cruz, Javier; López de la Cruz, Javier; Rapaport, Alain; Rapaport, Alain (Elsevier [Commercial Publisher], 2021-05-01)
In this corrigendum we correct an error in our paper [T. Caraballo, R. Colucci, J. López-de-la-Cruz and A. Rapaport. A way ...
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Statistical solutions and piecewise Liouville theorem for the impulsive reaction-diffusion equations on in nite latticesStatistical solutions and piecewise Liouville theorem for the impulsive reaction-diffusion equations on in nite lattices

Zhao, Caidi; Zhao, Caidi; Jiang, Huite; Jiang, Huite; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Elsevier, 2021-04-05)
We first verify the global well-posedness of the impulsive reaction-diffusion equations on infinite lattices. Then we ...
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Transportation inequalities for coupled systems of stochastic delay evolution equations with a fractional Brownian motionTransportation inequalities for coupled systems of stochastic delay evolution equations with a fractional Brownian motion

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Boudaoui, Ahmed; Boudaoui, Ahmed; Blouhi, Tayeb; Blouhi, Tayeb (Taylor and Francis Online, 2021-02-17)
We prove an existence and uniqueness result of mild solution for a system of stochastic semilinear differential equations ...
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On the Exponential Stability of Stochastic Perturbed Singular Systems in Mean SquareOn the Exponential Stability of Stochastic Perturbed Singular Systems in Mean Square

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ezzine, Faten; Ezzine, Faten; Hammami, Mohamed Ali; Hammami, Mohamed Ali (Springer, 2021-02-09)
The approach of Lyapunov functions is one of the most efficient ones for the investigation of the stability of stochastic ...
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Bounded random fluctuations on the input flow in chemostat models with wall growth and non-monotonic kineticsBounded random fluctuations on the input flow in chemostat models with wall growth and non-monotonic kinetics

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; López de la Cruz, Javier; López de la Cruz, Javier (AIMS Press, 2021-02-04)
This paper investigates a chemostat model with wall growth and Haldane consumption kinetics. In addition, bounded random ...
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Statistical solution and Liouville type theorem for the Klein-Gordon-Schrödinger equationsStatistical solution and Liouville type theorem for the Klein-Gordon-Schrödinger equations

Zhao, Caidi; Zhao, Caidi; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Lukaszewicz, Grzegorz; Lukaszewicz, Grzegorz (Elsevier [Commercial Publisher], Academic Press [Associate Organisation], 2021-01-28)
In this article, the authors investigate the system of Schr odinger and Klein-Gordon equations with Yukawa coupling. They ...
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Exponential behavior and upper noise excitation index of solutions to evolution equations with unbounded delay and tempered fractional Brownian motionsExponential behavior and upper noise excitation index of solutions to evolution equations with unbounded delay and tempered fractional Brownian motions

Wang, Yejuan; Wang, Yejuan; Liu, Yarong; Liu, Yarong; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Springer, 2021-01-02)
In this paper, we investigate stochastic evolution equations with unbounded delay in fractional power spaces perturbed by ...
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Exponential behavior and upper noise excitation index of solutions to evolution equations with unbounded delay and tempered fractional Brownian motionsExponential behavior and upper noise excitation index of solutions to evolution equations with unbounded delay and tempered fractional Brownian motions

Wang, Yejuan; Wang, Yejuan; Liu, Yarong; Liu, Yarong; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Springer, 2021-01-02)
In this paper, we investigate stochastic evolution equations with unbounded delay in fractional power spaces perturbed by ...
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Regularity of global attractors and exponential attractors for 2D quasi-geostrophic equations with fractional dissipationRegularity of global attractors and exponential attractors for 2D quasi-geostrophic equations with fractional dissipation

Yang, Lin; Yang, Lin; Wang, Yejuan; Wang, Yejuan; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (AIMS, 2021-01-01)
In this paper we investigate the regularity of global attractors and of exponential attractors for two dimensional ...
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Pullback exponential attractors for differential equations with delayPullback exponential attractors for differential equations with delay

Netchaoui, Sana; Netchaoui, Sana; Hammami, Mohamed Ali; Hammami, Mohamed Ali; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (American Institute of Mathematical Sciences, 2021-01-01)
We show the existence of an exponential attractor for non-autono-mous dynamical system with bounded delay. We considered ...
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The effect of a small bounded noise on the hyperbolicity for autonomous semilinear differential equationsThe effect of a small bounded noise on the hyperbolicity for autonomous semilinear differential equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Carvalho, Alexandre Nolasco; Carvalho, Alexandre Nolasco; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Oliveira Sousa, Alexandre N.; Oliveira Sousa, Alexandre N. (ScienceDirect, 2021-01-01)
In this work, we study permanence of hyperbolicity for autonomous differential equations under nonautonomous random/stochastic ...
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Stability of delay evolution equations with fading stochastic perturbationsStability of delay evolution equations with fading stochastic perturbations

Shaikhet, Leonid; Shaikhet, Leonid; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Taylor & Francis, 2020-12-08)
Stability of nonlinear delay evolution equation with stochastic perturbations is considered. It is shown that if the level ...
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Dynamics and numerical simulations to predict empirical antibiotic treatment of multi-resistant Pseudomonas aeruginosa infectionDynamics and numerical simulations to predict empirical antibiotic treatment of multi-resistant Pseudomonas aeruginosa infection

López de la Cruz, Javier; López de la Cruz, Javier; Pérez-Aranda Redondo, María; Pérez-Aranda Redondo, María; Alcudia Cruz, Ana; Alcudia Cruz, Ana; Begines Ruiz, Belén; Begines Ruiz, Belén; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Pajuelo Domínguez, Eloísa; Pajuelo Domínguez, Eloísa; Ginel Pérez, Pedro José; Ginel Pérez, Pedro José (Elsevier, 2020-12-01)
This work discloses an epidemiological mathematical model to predict an empirical treatment for dogs infected by Pseudomonas ...
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Invariant measures for the 3D globally modified Navier-Stokes equations with unbounded variable delaysInvariant measures for the 3D globally modified Navier-Stokes equations with unbounded variable delays

Wang, Jintao; Wang, Jintao; Zhao, Caidi; Zhao, Caidi; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Elsevier, 2020-12-01)
This article investigates the three-dimensional globally modified Navier-Stokes equations with unbounded variable delays. ...
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Asymptotically autonomous robustness of random attractors for a class of weakly dissipative stochastic wave equations on unbounded domainsAsymptotically autonomous robustness of random attractors for a class of weakly dissipative stochastic wave equations on unbounded domains

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Guo, Boling; Guo, Boling; Tuan, Nguyen Huy; Tuan, Nguyen Huy; Wang, Renhai; Wang, Renhai (Cambrigde Core, 2020-11-05)
This paper is concerned with the asymptotic behavior of solutions to a class of non-autonomous stochastic nonlinear wave ...
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Study of the chemostat model with non-monotonic growth under random disturbances on the removal rateStudy of the chemostat model with non-monotonic growth under random disturbances on the removal rate

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato; López de la Cruz, Javier; López de la Cruz, Javier; Rapaport, Alain; Rapaport, Alain (AIMS Press, 2020-10-29)
We revisit the chemostat model with Haldane growth function, here subject to bounded random disturbances on the input flow ...
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Dynamics of a stochastic coronavirus (COVID-19) epidemic model with Markovian switchingDynamics of a stochastic coronavirus (COVID-19) epidemic model with Markovian switching

Boukanjime, Brahim; Boukanjime, Brahim; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; El Fatini, Mohamed; El Fatini, Mohamed; El Khalifi, Mohamed; El Khalifi, Mohamed (Elsevier, 2020-10-16)
In this paper, we analyze a stochastic coronavirus (COVID-19) epidemic model which is perturbed by both white noise and ...
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Non-autonomous nonlocal partial differential equations with delay and memoryNon-autonomous nonlocal partial differential equations with delay and memory

Xu, Jiaohui; Xu, Jiaohui; Zhang, Zhengce; Zhang, Zhengce; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Elsevier [Commercial Publisher], Academic Press [Associate Organisation], 2020-09-15)
The paper addresses a kind of non-autonomous nonlocal parabolic equations when the external force contains hereditary ...
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Stability of fractionally dissipative 2D quasi-geostrophic equation with infinite delayStability of fractionally dissipative 2D quasi-geostrophic equation with infinite delay

Liang, Tongtong; Liang, Tongtong; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Wang, Yejuan; Wang, Yejuan (Springer, 2020-08-18)
In this paper, fractionally dissipative 2D quasi-geostrophic equations with an external force containing infinite delay ...
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Morse decomposition for gradient-like multi-valued autonomous and nonautonomous dynamical systemsMorse decomposition for gradient-like multi-valued autonomous and nonautonomous dynamical systems

Wang, Yejuan; Wang, Yejuan; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (American Institute of Mathematical Sciences (AIMS), 2020-08-01)
In this paper, we first prove that the property of being a gradientlike general dynamical system and the existence of a ...
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On initial value and terminal value problems for subdiffusive stochastic Rayleigh-Stokes equationOn initial value and terminal value problems for subdiffusive stochastic Rayleigh-Stokes equation

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ngoc, Tran Bao; Ngoc, Tran Bao; Thach, Tran Ngoc; Thach, Tran Ngoc; Tuan, Nguyen Huy; Tuan, Nguyen Huy (AIMS, 2020-06-30)
In this paper, we study two stochastic problems for time-fractional RayleighStokes equation including the initial value ...
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Long time dynamics for functional three-dimensional Navier-Stokes-Voigt equationsLong time dynamics for functional three-dimensional Navier-Stokes-Voigt equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Márquez Durán, Antonio Miguel; Márquez Durán, Antonio Miguel (AIMS PressAIMS Press, 2020-06-24)
In this paper we consider a non-autonomous Navier-Stokes-Voigt model including a variety of delay terms in a unified ...
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ON INITIAL AND TERMINAL VALUE PROBLEMS FOR FRACTIONAL NONCLASSICAL DIFFUSION EQUATIONSON INITIAL AND TERMINAL VALUE PROBLEMS FOR FRACTIONAL NONCLASSICAL DIFFUSION EQUATIONS

NGuyen, Huy Tuan; NGuyen, Huy Tuan; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (American Mathematical Society, 2020-06-11)
In this paper, we consider fractional nonclassical diffusion equations under two forms: initial value problem and terminal ...
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Robustness of exponential dichotomy in a class of generalised almost periodic linear differential equations in infinite dimensional Banach spacesRobustness of exponential dichotomy in a class of generalised almost periodic linear differential equations in infinite dimensional Banach spaces

Rodrígues, H. M.; Rodrígues, H. M.; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Nakassima, G. K.; Nakassima, G. K. (Springer, 2020-06-05)
In this paper we study the robustness of the exponential dichotomy in nonautonomous linear ordinary differential equations ...
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Trajectory statistical solutions and Liouville type equations for evolution equations: abstract results and applicationsTrajectory statistical solutions and Liouville type equations for evolution equations: abstract results and applications

Zhao, Caidi; Zhao, Caidi; Li, Yanjiao; Li, Yanjiao; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Elsevier, 2020-06-01)
In this article, we first prove, from the viewpoint of infinite dynamical system, sufficient conditions ensuring the ...
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A free boundary tumor model with time dependent nutritional supplyA free boundary tumor model with time dependent nutritional supply

Sun, Wenlong; Sun, Wenlong; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Han, Xiaoying; Han, Xiaoying; Kloeden, Peter E.; Kloeden, Peter E. (Elsevier, 2020-06-01)
A non-autonomous free boundary model for tumor growth is studied. The model consists of a nonlinear reaction diffusion ...
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A contribution to the analysis of time fractional stochastic functional partial differential equations and applicationsA contribution to the analysis of time fractional stochastic functional partial differential equations and applications

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Xu, Jiaohui; Xu, Jiaohui (2020-05-20)
On the one hand, the classical heat equation∂tu= ∆udescribes heatpropagation in a homogeneous medium, while the time ...
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A STOCHASTIC THRESHOLD FOR AN EPIDEMIC MODEL WITH ISOLATION AND A NON LINEAR INCIDENCEA STOCHASTIC THRESHOLD FOR AN EPIDEMIC MODEL WITH ISOLATION AND A NON LINEAR INCIDENCE

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; El Fatini, Mohamed; El Fatini, Mohamed; Sekkak, Idriss; Sekkak, Idriss; Taki, Regragui; Taki, Regragui; Laaribi, Aziz; Laaribi, Aziz (AIMS Press, 2020-05-01)
In this paper, we study a stochastic epidemic model with isolation and nonlinear incidence. In particular, we propose a ...
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Dynamical systems applied to consciousness and brain rhythms in a neural networkDynamical systems applied to consciousness and brain rhythms in a neural network

Langa Rosado, José Antonio; Langa Rosado, José Antonio; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Galadí García, Javier Alejandro; Galadí García, Javier Alejandro (2020-04-21)
This thesis applies the great advances of modern dynamical systems theory (DST) to consciousness. Consciousness, or ...
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Analysis of a stochastic distributed delay epidemic model with relapse and Gamma distribution kernelAnalysis of a stochastic distributed delay epidemic model with relapse and Gamma distribution kernel

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; El Fatini, Mohamed; El Fatini, Mohamed; El Khalifi, Mohamed; El Khalifi, Mohamed; Gerlach, Richard; Gerlach, Richard; Pettersson, Roger; Pettersson, Roger (Elsevier, 2020-04-01)
In this work, we investigate a stochastic epidemic model with relapse and distributed delay. First, we prove that our model ...
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STABILITY ANALYSIS OF A DELAY DIFFERENTIAL KALDOR’S MODEL WITH GOVERNMENT POLICIESSTABILITY ANALYSIS OF A DELAY DIFFERENTIAL KALDOR’S MODEL WITH GOVERNMENT POLICIES

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Pereira da Silva, Alex; Pereira da Silva, Alex (Mathematica Scandinavica [Independent Journal], 2020-03-29)
This paper is devoted to analyze the stability of the economy according to an extended version of Kaldor's economic growth ...
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Existence and exponential stability for neutral stochastic integro-differential equations with impulses driven by a Rosenblatt processExistence and exponential stability for neutral stochastic integro-differential equations with impulses driven by a Rosenblatt process

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ogouyandjou, Carlos; Ogouyandjou, Carlos; Allognissode, Fulbert Kuessi; Allognissode, Fulbert Kuessi; Diop, Mamadou Abdoul; Diop, Mamadou Abdoul (American Institute of Mathematical Sciences (AIMS), 2020-02-01)
The existence and uniqueness of mild solution of an impulsive stochastic system driven by a Rosenblatt process is analyzed ...
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Strong trajectory statistical solutions and Liouville type equation for dissipative Euler equationsStrong trajectory statistical solutions and Liouville type equation for dissipative Euler equations

Zhao, Caidi; Zhao, Caidi; Song, Zhongchun; Song, Zhongchun; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Elsevier, 2020-01-01)
The main aim of this letter is to use the strong compact strong trajectory attractor to construct the strong trajectory ...
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Stability results for neutral stochastic functional differential equations via fixed point methodsStability results for neutral stochastic functional differential equations via fixed point methods

Benhadri, Mimia; Benhadri, Mimia; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Zeghdoudi, Halim; Zeghdoudi, Halim (Taylor and Francis, 2020-01-01)
In this paper we prove some results on the mean square asymptotic stability of a class of neutral stochastic differential ...
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Mathematical methods for the randomized non-autonomous Bertalanffy modelMathematical methods for the randomized non-autonomous Bertalanffy model

Calatayud Gregori, Julia; Calatayud Gregori, Julia; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Cortés López, Juan Carlos; Cortés López, Juan Carlos; Jornet Sanz, Marc; Jornet Sanz, Marc (Texas State University, 2020-01-01)
In this article we analyze the randomized non-autonomous Bertalanffy model x 0 (t, ω) = a(t, ω)x(t, ω) + b(t, ω)x(t, ω) 2/3, ...
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Existence of periodic positive solutions to a nonlinear Lotka-Votlerra competition systemsExistence of periodic positive solutions to a nonlinear Lotka-Votlerra competition systems

Benhadri, Mimia; Benhadri, Mimia; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Zeghdoudi, Halim; Zeghdoudi, Halim (AGH University of Science and Technology Press, 2020-01-01)
We investigate the existence of positive periodic solutions of a nonlinear Lotka-Volterra competition system with deviating ...
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Extremal bounded complete trajectories for nonautonomous reaction-diffusion equations with discontinuous forcing termExtremal bounded complete trajectories for nonautonomous reaction-diffusion equations with discontinuous forcing term

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Valero Cuadra, José; Valero Cuadra, José (Springer, 2020-01-01)
In this paper we establish a strong comparison principle for a nonautonomous differential inclusion with a forcing term ...
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Minimizing the expected time to detect a randomly located lost target using 3-dimensional search techniqueMinimizing the expected time to detect a randomly located lost target using 3-dimensional search technique

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Teamah, Abd El-Moneim Anwar; Teamah, Abd El-Moneim Anwar; El-Bagoury, Abd Al-Aziz Hosni; El-Bagoury, Abd Al-Aziz Hosni (Taylor and Francis, 2020-01-01)
This paper considers a new model in search theory to find a randomly located target in the 3-dimensional space. An ...
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Practical stability with respect to a part of variables of stochastic differential equationsPractical stability with respect to a part of variables of stochastic differential equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ezzine, Faten; Ezzine, Faten; Hammami, Mohamed Ali; Hammami, Mohamed Ali; Mchiri, Lassaad; Mchiri, Lassaad (Taylor & Francis, 2020-01-01)
In this paper, practical stability with respect to a part of the variables of nonlinear stochastic differential equations ...
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Upper and Lower Semicontinuity of Impulsive Cocycle Attractors for Impulsive Nonautonomous SystemsUpper and Lower Semicontinuity of Impulsive Cocycle Attractors for Impulsive Nonautonomous Systems

Bonotto, Everaldo de Mello; Bonotto, Everaldo de Mello; Bortolan, Matheus Cheque; Bortolan, Matheus Cheque; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Collegari, Rodolfo; Collegari, Rodolfo (Springer, 2019-12-05)
In this work we present results to ensure a weak upper semicontinuity for a family of impulsive cocycle attractors of ...
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Analysis of a stochastic 2D–Navier-Stokes model with infinite delayAnalysis of a stochastic 2D–Navier-Stokes model with infinite delay

Liu, Linfang; Liu, Linfang; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Springer, 2019-12-01)
Some results concerning a stochastic 2D Navier-Stokes system when the external forces contain hereditary characteristics ...
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Mild Solutions to Time Fractional Stochastic 2D-Stokes Equations with Bounded and Unbounded DelayMild Solutions to Time Fractional Stochastic 2D-Stokes Equations with Bounded and Unbounded Delay

Xu, Jiaohui; Xu, Jiaohui; Zhang, Zhengce; Zhang, Zhengce; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Springer, 2019-11-19)
In this paper, the well-posedness of stochastic time fractional 2D-Stokes equations of order α ∈ (0, 1) containig finite ...
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Existence and regularity results for terminal value problem for nonlinear fractional wave equationsExistence and regularity results for terminal value problem for nonlinear fractional wave equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Tuan, Nguyen Huy; Tuan, Nguyen Huy; Ngoc, Tran Bao; Ngoc, Tran Bao; Zhou, Yong; Zhou, Yong (IOP Science, 2019-11-15)
We consider the terminal value problem (or called nal value problem, initial inverse prob- lem, backward in time problem) ...
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A way to model stochastic perturbations in population dynamics models with bounded realizationsA way to model stochastic perturbations in population dynamics models with bounded realizations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato; López de la Cruz, Javier; López de la Cruz, Javier; Rapaport, Alain; Rapaport, Alain (Elsevier, 2019-10-01)
In this paper, we analyze the use of the Ornstein-Uhlenbeck process to model dynamical systems subjected to bounded noisy ...
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On the asymptotic behavior of highly nonlinear hybrid stochastic delay differential equationsOn the asymptotic behavior of highly nonlinear hybrid stochastic delay differential equations

Zhang, Tian; Zhang, Tian; Chen, Huabin; Chen, Huabin; Yuan, Chenggui; Yuan, Chenggui; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (American Institute of Mathematical Sciences, 2019-10-01)
In this paper, under a local Lipschitz condition and a monotonicity condition, the problems on the existence and uniqueness ...
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Resolubility of linear Cauchy problems on Fréchet spaces and a delayed Kaldor’s modelResolubility of linear Cauchy problems on Fréchet spaces and a delayed Kaldor’s model

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Pereira da Silva, Alex; Pereira da Silva, Alex (2019-09-06)
The long-run aim of this thesis is to solve delay differential equations with infinite delay of the type d dt u(t) = ...
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Hyers-Ulam stability for coupled random fixed point theorems and applications to periodic boundary value random problemsHyers-Ulam stability for coupled random fixed point theorems and applications to periodic boundary value random problems

Boudaoui, Ahmed; Boudaoui, Ahmed; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Blouhi, Tayeb; Blouhi, Tayeb (De Gruyter, 2019-09-01)
In this paper, we prove some existence, uniqueness and Hyers-Ulam stability results for the coupled random fixed point of ...
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Applying the random variable transformation method to solve a class of random linear differential equation with discrete delayApplying the random variable transformation method to solve a class of random linear differential equation with discrete delay

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Cortés López, Juan Carlos; Cortés López, Juan Carlos; Navarro Quilés, Ana; Navarro Quilés, Ana (Elsevier, 2019-09-01)
We randomize the following class of linear differential equations with delay, x 0 τ (t) = axτ(t) + bxτ(t − τ), t > 0, and ...
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Trajectory and global attractors for generalized processesTrajectory and global attractors for generalized processes

Samprogna, Rodrigo Antonio; Samprogna, Rodrigo Antonio; Gentile Mossa, Claudia Buttarello; Gentile Mossa, Claudia Buttarello; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Schiabel, Karina; Schiabel, Karina (American Institute of Mathematical Sciences, 2019-08-01)
In this work the theory of generalized processes is used to describe the dynamics of a nonautonomous multivalued problem ...
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Well-posedness and dynamics of impulsive fractional stochastic evolution equations with unbounded delayWell-posedness and dynamics of impulsive fractional stochastic evolution equations with unbounded delay

Xu, Jiaohui; Xu, Jiaohui; Zhang, Zhengce; Zhang, Zhengce; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Elsevier, 2019-08-01)
This paper is concerned with the well-posedness and dynamics of delay impulsive fractional stochastic evolution equations ...
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Modeling and analysis of random and stochastic input flows in the chemostat modelModeling and analysis of random and stochastic input flows in the chemostat model

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; López de la Cruz, Javier; López de la Cruz, Javier (American Institute of Mathematical Sciences, 2019-08-01)
In this paper we study a new way to model noisy input flows in the chemostat model, based on the Ornstein-Uhlenbeck process. ...
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The asymptotic behaviour of fractional lattice systems with variable delayThe asymptotic behaviour of fractional lattice systems with variable delay

Liu, Linfang; Liu, Linfang; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E. (De Gruyter, 2019-06-01)
The existence and uniqueness of global solutions for a fractional functional differential equation is established. The ...
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Global stability and positive recurrence of a stochastic SIS model with Lévy noise perturbationGlobal stability and positive recurrence of a stochastic SIS model with Lévy noise perturbation

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Settati, Adel; Settati, Adel; El Fatini, Mohamed; El Fatini, Mohamed; Lahrouz, Aadil; Lahrouz, Aadil; Imlahi, Abdelouahid; Imlahi, Abdelouahid (Elsevier, 2019-06-01)
Focusing on epidemic model in random environments, this paper uses white noise and Lévy noise to model the dynamics of the ...
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Bifurcation scenarios in an ordinary differential equation with constant and distributed delay: A case studyBifurcation scenarios in an ordinary differential equation with constant and distributed delay: A case study

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato; Guerrini, Luca; Guerrini, Luca (American Institute of Mathematical, 2019-06-01)
In this article we consider a model introduced by Ucar in order to simply describe chaotic behaviour with a one dimensional ...
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Long time behavior of fractional impulsive stochastic differential equations with infinite delayLong time behavior of fractional impulsive stochastic differential equations with infinite delay

Xu, Jiaohui; Xu, Jiaohui; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (American Institute of Mathematical Sciences, 2019-06-01)
This paper is first devoted to the local and global existence of mild solutions for a class of fractional impulsive ...
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Asymptotic regularity of trajectory attractor and trajectory statistical solution for the 3D globally modified Navier-Stokes equationsAsymptotic regularity of trajectory attractor and trajectory statistical solution for the 3D globally modified Navier-Stokes equations

Zhao, Caidi; Zhao, Caidi; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Elsevier, 2019-05-15)
We first prove the existence and regularity of the trajectory attractor for a threedimensional system of globally modified ...
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Some remarks on an environmental defensive expenditures modelSome remarks on an environmental defensive expenditures model

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato; Guerrini, Luca; Guerrini, Luca (American Institute of Mathematical Sciences, 2019-03-01)
In this paper, we consider the environmental defensive expenditures model with delay proposed by Russu in P. Russu, Hopf ...
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Dynamic safety assessment of a nonlinear pumped-storage generating system in a transient processDynamic safety assessment of a nonlinear pumped-storage generating system in a transient process

Li, Huanhuan; Li, Huanhuan; Chen, Diyi; Chen, Diyi; Arzaghi, Ehsan; Arzaghi, Ehsan; Abbassi, Rouzbeh; Abbassi, Rouzbeh; Kilicman, Adem; Kilicman, Adem; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Patelli, Edoardo; Patelli, Edoardo; Gao, Xiang; Gao, Xiang; Xu, Beibei; Xu, Beibei (Elsevier, 2019-02-01)
This paper focuses on a pumped-storage generating system with a reversible Francis turbine and presents an innovative ...
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Topological method for coupled systems of impulsive stochastic semilinear differential inclusions with fractional Brownian motionTopological method for coupled systems of impulsive stochastic semilinear differential inclusions with fractional Brownian motion

Blouhi, Tayeb; Blouhi, Tayeb; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ouahab, Abdelghani; Ouahab, Abdelghani (Casa Cărţii de Ştiinţă Cluj-Napoca, 2019-02-01)
In this paper we prove the existence of mild solutions for a first-order impulsive semilinear stochastic differential ...
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Existence of solutions and stability for impulsive neutral stochastic functional differential equationsExistence of solutions and stability for impulsive neutral stochastic functional differential equations

Benhadri, Mimia; Benhadri, Mimia; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Zeghdoudi, Halim; Zeghdoudi, Halim (Taylor & Franci, 2019-01-01)
In this paper we prove some results on the existence of solutions and the mean square asymptotic stability for a class of ...
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Stability results for 2D Navier-Stokes equations with unbounded delayStability results for 2D Navier-Stokes equations with unbounded delay

Liu, Linfang; Liu, Linfang; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Marín Rubio, Pedro; Marín Rubio, Pedro (Elsevier, 2018-12-05)
Some results related to 2D Navier-Stokes equations when the external force contains hereditary characteristics involving ...
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Exponential stability of an incompressible non-Newtonian fluid with delayExponential stability of an incompressible non-Newtonian fluid with delay

Liu, Linfang; Liu, Linfang; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Fu, Xianlong; Fu, Xianlong (American Institute of Mathematical Sciences, 2018-12-01)
The existence and uniqueness of stationary solutions to an incompressible non-Newtonian fluid are first established. The ...
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Global and cocycle attractors for non-autonomous reaction-diffusion equations. The case of null upper Lyapunov exponentGlobal and cocycle attractors for non-autonomous reaction-diffusion equations. The case of null upper Lyapunov exponent

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Obaya García, Rafael; Obaya García, Rafael; Sanz Gil, Ana María; Sanz Gil, Ana María (Elsevier, 2018-11-05)
In this paper we obtain a detailed description of the global and cocycle attractors for the skew-product semiflows induced ...
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Time-dependent attractors for non-autonomous nonlocal reaction-diffusion equationsTime-dependent attractors for non-autonomous nonlocal reaction-diffusion equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Herrera Cobos, Marta; Herrera Cobos, Marta; Marín Rubio, Pedro; Marín Rubio, Pedro (Cambridge University Press, 2018-10-01)
In this paper, the existence and uniqueness of weak and strong solutions for a non-autonomous nonlocal reaction-diffusion ...
PhD Thesis
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Sistemas dinámicos en modelos estocásticos con ruido fraccionario.Sistemas dinámicos en modelos estocásticos con ruido fraccionario.

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; López de la Cruz, Javier; López de la Cruz, Javier (2018-06-28)
PhD Thesis
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Analysis of infinite dimensional dynamical systems associated to functional differential equations.Analysis of infinite dimensional dynamical systems associated to functional differential equations.

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Liu, Linfang; Liu, Linfang (2018-06-28)
Based on the theory of functional diferential equations, theory of semigroup, theory of random dynamical systems and theory ...
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Robustness of time-dependent attractors in H1-norm for nonlocal problemsRobustness of time-dependent attractors in H1-norm for nonlocal problems

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Herrera Cobos, Marta; Herrera Cobos, Marta; Marín Rubio, Pedro; Marín Rubio, Pedro (American Institute of Mathematical Sciences, 2018-05-01)
In this paper, the existence of regular pullback attractors as well as their upper semicontinuous behaviour in H1-norm are ...
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Asymptotic behaviour of nonlocal p-Laplacian reaction-diffusion problemsAsymptotic behaviour of nonlocal p-Laplacian reaction-diffusion problems

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Herrera Cobos, Marta; Herrera Cobos, Marta; Marín Rubio, Pedro; Marín Rubio, Pedro (Elsevier, 2018-03-01)
In this paper, we focus on studying the existence of attractors in the phase spaces L2(Ω) and Lp(Ω) (among others) for ...
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Analysis of a stochastic SIR model with fractional Brownian motionAnalysis of a stochastic SIR model with fractional Brownian motion

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Keraani, Sami; Keraani, Sami (Taylor & Francis, 2018-01-01)
In this article, a stochastic version of a SIR nonautonomous model previously introduced in Kloeden and Kozyakin (2011) ...
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A stochastic SIRI epidemic model with relapse and media coverageA stochastic SIRI epidemic model with relapse and media coverage

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; El Fatini, Mohamed; El Fatini, Mohamed; Pettersson, Roger; Pettersson, Roger; Taki, Regragui; Taki, Regragui (American Institute of Mathematical Sciences, 2018-01-01)
This work is devoted to investigate the existence and uniqueness of a global positive solution for a stochastic epidemic ...
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A stochastic SIRI epidemic model with Lévy noiseA stochastic SIRI epidemic model with Lévy noise

Berrhazi, Badr-eddine; Berrhazi, Badr-eddine; El Fatini, Mohamed; El Fatini, Mohamed; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Pettersson, Roger; Pettersson, Roger (American Institute of Mathematical Sciences, 2018-01-01)
Some diseases such as herpes, bovine and human tuberculosis exhibit relapse in which the recovered individuals do not ...
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On a predator prey model with nonlinear harvesting and distributed delayOn a predator prey model with nonlinear harvesting and distributed delay

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato; Guerrini, Luca; Guerrini, Luca (American Institute of Mathematical Sciences, 2018-01-01)
A predator prey model with nonlinear harvesting (Holling type-II) with both constant and distributed delay is considered. ...
Final Degree Project
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Aplicación de los sistemas diferenciales al estudio de un modelo epidemiológico con reinfecciónAplicación de los sistemas diferenciales al estudio de un modelo epidemiológico con reinfección

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Lindes Colón, Mercedes; Lindes Colón, Mercedes (2018-01-01)
Mathematical modeling, currently, is a very important element in health system, since it allows studying the incidence, ...
Presentation
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Pullback attractors to analyze the effect of random and stochastic disturbances in the chemostat modelPullback attractors to analyze the effect of random and stochastic disturbances in the chemostat model

López de la Cruz, Javier; López de la Cruz, Javier; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; Rapaport, Alain; Rapaport, Alain (2018-01-01)
In this talk, some random and stochastic disturbances in the chemostat model will be analyzed by making use of the modern ...
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Dynamic evolution of a hydraulic-mechanical-electric system with randomly fluctuating speed based on Chebyshev polynomial approximation methodDynamic evolution of a hydraulic-mechanical-electric system with randomly fluctuating speed based on Chebyshev polynomial approximation method

Xu, Beibei; Xu, Beibei; Chen, Diyi; Chen, Diyi; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Springer, 2018-01-01)
The research proposed in this paper focuses on the dynamic evolution of a hydraulic-mechanical-electric system under the ...
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Dynamics of a continuous Hénon modelDynamics of a continuous Hénon model

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato; Guerrini, Luca; Guerrini, Luca (Wiley, 2018-01-01)
We study a continuous Hénon system obtained by considering the discrete original model in continuous time. While the ...
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Pullback attractor for a dynamic boundary non-autonomous problem with Infinite delayPullback attractor for a dynamic boundary non-autonomous problem with Infinite delay

Samprogna, Rodrigo Antonio; Samprogna, Rodrigo Antonio; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (American Institute of Mathematical Sciences, 2018-01-01)
In this work we prove the existence of solution for a p-Laplacian non-autonomous problem with dynamic boundary and infinite ...
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Random pullback exponential attractors: general existence results for random dynamical systems in Banach spacesRandom pullback exponential attractors: general existence results for random dynamical systems in Banach spaces

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Sonner, Stefanie; Sonner, Stefanie (American Institute of Mathematical Sciences, 2017-12-01)
We derive general existence theorems for random pullback exponential attractors and deduce explicit bounds for their fractal dimension. The results are formulated for asymptotically compact random dynamical systems in Banach spaces.
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Dynamics of a class of ODEs via waveletsDynamics of a class of ODEs via wavelets

Munhoz Rodrigues, Hildebrando; Munhoz Rodrigues, Hildebrando; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Fuzeto Gameiro, Marcio; Fuzeto Gameiro, Marcio (American Institute of Mathematical Sciences, 2017-11-01)
The objective of this paper is to study a perturbed linear hyperbolic differential equation. The first part of this work ...
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Practical exponential stability of impulsive stochastic functional differential equationsPractical exponential stability of impulsive stochastic functional differential equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Hammami, Mohamed Ali; Hammami, Mohamed Ali; Mchiri, Lassaad; Mchiri, Lassaad (Elsevier, 2017-11-01)
This paper is devoted to the investigation of the practical exponential stability of impulsive stochastic functional ...
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Well-posedness and dynamics of a fractional stochastic integro-differential equationWell-posedness and dynamics of a fractional stochastic integro-differential equation

Liu, Linfang; Liu, Linfang; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Elsevier, 2017-09-15)
In this paper we investigate the well-posedness and dynamics of a fractional stochastic integro-differential equation ...
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Stochastic differential equations with non-instantaneous impulses driven by a fractional Brownian motionStochastic differential equations with non-instantaneous impulses driven by a fractional Brownian motion

Boudaoui, Ahmed; Boudaoui, Ahmed; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (American Institute of Mathematical Sciences, 2017-09-01)
This paper is concerned with the existence and continuous dependence of mild solutions to stochastic differential equations ...
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Long time behavior of stochastic parabolic problems with white noise in materials with thermal memoryLong time behavior of stochastic parabolic problems with white noise in materials with thermal memory

Liu, Linfang; Liu, Linfang; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E. (Springer, 2017-09-01)
The existence and limiting behavior of the solutions of stochastic parabolic problems with thermal memory are investigate ...
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Dynamics of some stochastic chemostat models with multiplicative noiseDynamics of some stochastic chemostat models with multiplicative noise

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; López de la Cruz, Javier; López de la Cruz, Javier (American Institute of Mathematical Sciences, 2017-08-01)
In this paper we study two stochastic chemostat models, with and without wall growth, driven by a white noise. Specifically, ...
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Corrigendum to the paper: Existence and stability results for semilinear systems of impulsivestochastic differential equations with fractionalBrownian motion. Stoch. Anal. Appl. 34 (2016), no. 5, 792–834Corrigendum to the paper: Existence and stability results for semilinear systems of impulsivestochastic differential equations with fractionalBrownian motion. Stoch. Anal. Appl. 34 (2016), no. 5, 792–834

Blouhi, Tayeb; Blouhi, Tayeb; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ouahab, Abdelghani; Ouahab, Abdelghani (Taylor & Francis, 2017-08-01)
In this paper we correct an error made in our paper [Blouhi, T.; Caraballo, T.; Ouahab, A. Existence and stability results ...
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Global attractor for a nonlocal p-Laplacian equation without uniqueness of solutionGlobal attractor for a nonlocal p-Laplacian equation without uniqueness of solution

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Herrera Cobos, Marta; Herrera Cobos, Marta; Marín Rubio, Pedro; Marín Rubio, Pedro (American Institute of Mathematical Sciences, 2017-07-01)
In this paper, the existence of solution for a p-Laplacian parabolic equation with nonlocal diffusion is established. To ...
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Asymptotic behaviour of a non-classical and non-autonomous diffusion equation containing some hereditary characteristicAsymptotic behaviour of a non-classical and non-autonomous diffusion equation containing some hereditary characteristic

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Márquez Durán, Antonio Miguel; Márquez Durán, Antonio Miguel; Rivero Garvía, Luis Felipe; Rivero Garvía, Luis Felipe (American Institute of Mathematical Sciences, 2017-07-01)
We show existence and uniqueness of solutions for a non-classical and non-autonomous diffusion equation with infinite delay ...
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Attractors for a random evolution equation with infinite memory: Theoretical resultsAttractors for a random evolution equation with infinite memory: Theoretical results

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; Schmalfuss, Björn; Schmalfuss, Björn; Valero Cuadra, José; Valero Cuadra, José (American Institute of Mathematical Sciences, 2017-07-01)
The long-time behavior of solutions (more precisely, the existence of random pullback attractors) for an integro-differential ...
Final Degree Project
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Ecuaciones diferenciales con retardo: Aplicación a un modelo de quimiostatoEcuaciones diferenciales con retardo: Aplicación a un modelo de quimiostato

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Ruiz González, Ángeles; Ruiz González, Ángeles (2017-06-01)
In this work we will study the theory of dynamical systems with application to a chemostat. Starting with the autonomous ...
Final Degree Project
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Estudio del comportamiento asintótico de un modelo en epidemiologíaEstudio del comportamiento asintótico de un modelo en epidemiología

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Minuesa Abril, María José; Minuesa Abril, María José (2017-06-01)
Nowadays, mathematical models are one of the most popular tools to study epidemics due to the fact that they enable to ...
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A qualitative description of microstructure formation and coarsening phenomena for an evolution equationA qualitative description of microstructure formation and coarsening phenomena for an evolution equation

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato (Springer, 2017-04-01)
We provide a qualitative description of microstructure formation and coarsening phenomena for the solutions of a singularly ...
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Attractors for impulsive non-autonomous dynamical systems and their relationsAttractors for impulsive non-autonomous dynamical systems and their relations

Bonotto, Everaldo de Mello; Bonotto, Everaldo de Mello; Bortolan, Matheus Cheque; Bortolan, Matheus Cheque; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Collegari, Rodolfo; Collegari, Rodolfo (Elsevier, 2017-03-15)
In this work, we deal with several different notions of attractors that may appear in the impulsive non-autonomous case ...
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Stabilization of oscillations in a phase transition modelStabilization of oscillations in a phase transition model

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato (Wiley, 2017-02-01)
In this paper we analyze a model presenting formation of microstructure depending on the parameters and the initial data. ...
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A comparison between random and stochastic modeling for a SIR modelA comparison between random and stochastic modeling for a SIR model

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato (American Institute of Mathematical Sciences, 2017-01-01)
In this article, a random and a stochastic version of a SIR nonautonomous model previously introduced in P. E. Kloeden and ...
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Dynamics of a non-autonomous incompressible non-Newtonian fluid with delayDynamics of a non-autonomous incompressible non-Newtonian fluid with delay

Liu, Linfang; Liu, Linfang; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Fu, Xianlong; Fu, Xianlong (International Press, 2017-01-01)
We first study the well-posedness of a non-autonomous incompressible non-Newtonian fluid with delay. The existence of ...
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Pullback, forward and chaotic dynamics in 1-D non-autonomous linear-dissipative equationsPullback, forward and chaotic dynamics in 1-D non-autonomous linear-dissipative equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Obaya García, Rafael; Obaya García, Rafael (IOP Publishing, 2017-01-01)
The global attractor of a skew product semiflow for a non-autonomous differential equation describes the asymptotic behaviour ...
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Random dynamical systems to analyze different ways of modeling stochastic chemostatsRandom dynamical systems to analyze different ways of modeling stochastic chemostats

López de la Cruz, Javier; López de la Cruz, Javier; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; Rapaport, Alain; Rapaport, Alain (2017-01-01)
In this talk, some different ways of modeling stochastic chemostats will be presented in order to obtain much more realistic ...
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Existence and asymptotic behavior of solutions for neutral stochastic partial integrodifferential equations with infinite delaysExistence and asymptotic behavior of solutions for neutral stochastic partial integrodifferential equations with infinite delays

Diop, Mamadou Abdoul; Diop, Mamadou Abdoul; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Zene, Mahamat Mahamat; Zene, Mahamat Mahamat (World Scientific Publishing, 2016-12-01)
In this work we study the existence, uniqueness and asymptotic behavior of mild solutions for neutral stochastic partial ...
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Equi-attraction and continuity of attractors for skew-product semiflowsEqui-attraction and continuity of attractors for skew-product semiflows

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Carvalho, Alexandre Nolasco; Carvalho, Alexandre Nolasco; Barbosa da Costa, Henrique; Barbosa da Costa, Henrique; Langa Rosado, José Antonio; Langa Rosado, José Antonio (American Institute of Mathematical Sciences, 2016-11-01)
In this paper we prove the equivalence between equi-attraction and continuity of attractors for skew-product semi-flows, ...
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Mild solutions of non-Lipschitz stochastic integrodifferential evolution equationsMild solutions of non-Lipschitz stochastic integrodifferential evolution equations

Diop, Mamadou Abdoul; Diop, Mamadou Abdoul; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Mané, Aziz; Mané, Aziz (Wiley, 2016-10-01)
In this work we study the existence and uniqueness of mild solutions for stochastic partial integrodifferential equations ...
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Non-autonomous dynamics of a semi-Kolmogorov population model with periodic forcingNon-autonomous dynamics of a semi-Kolmogorov population model with periodic forcing

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato; Han, Xiaoying; Han, Xiaoying (Elsevier, 2016-10-01)
In this paper we study a semi-Kolmogorov type of population model, arising from a predator-prey system with indirect ...
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Impulsive surfaces on dynamical systemsImpulsive surfaces on dynamical systems

Bonotto, Everaldo de Mello; Bonotto, Everaldo de Mello; Bortolan, Matheus Cheque; Bortolan, Matheus Cheque; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Collegari, Rodolfo; Collegari, Rodolfo (Springer, 2016-10-01)
This work is devoted to the construction of impulsive sets in Rn. In the literature, there are many examples of impulsive ...
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Semi-Kolmogorov models for predation with indirect effects in random environmentsSemi-Kolmogorov models for predation with indirect effects in random environments

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato (American Institute of Mathematical Sciences, 2016-09-01)
In this work we study semi-Kolmogorov models for predation with both the carrying capacities and the indirect effects ...
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Structure of the pullback attractor for a non-autonomous scalar differential inclusionStructure of the pullback attractor for a non-autonomous scalar differential inclusion

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio (American Institute of Mathematical Sciences, 2016-08-01)
The structure of attractors for differential equations is one of the main topics in the qualitative theory of dynamical ...
PhD Thesis
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Comportamiento asintótico en tiempo de ecuaciones en derivadas parciales no localesComportamiento asintótico en tiempo de ecuaciones en derivadas parciales no locales

Marín Rubio, Pedro; Marín Rubio, Pedro; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Herrera Cobos, Marta; Herrera Cobos, Marta (2016-06-23)
En las últimas décadas muchos investigadores han estado interesados en estudiar problemas no locales por su utilidad en ...
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Impulsive stochastic functional differential inclusions driven by a fractional Brownian motion with infinite delayImpulsive stochastic functional differential inclusions driven by a fractional Brownian motion with infinite delay

Boudaoui, Ahmed; Boudaoui, Ahmed; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ouahab, Abdelghani; Ouahab, Abdelghani (Wiley, 2016-04-01)
In this paper, we prove the existence of mild solutions for the following first-order impulsive semilinear stochastic ...
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Existence and stability results for semilinear systems of impulsive stochastic differential equations with fractional Brownian motionExistence and stability results for semilinear systems of impulsive stochastic differential equations with fractional Brownian motion

Blouhi, Tayeb; Blouhi, Tayeb; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ouahab, Abdelghani; Ouahab, Abdelghani (Taylor & Francis, 2016-01-01)
Some results on the existence and uniqueness of mild solution for a system of semilinear impulsive differential equations ...
Book
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Applied nonautonomous and random dynamical systemsApplied nonautonomous and random dynamical systems

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Han, Xiaoying; Han, Xiaoying (Springer, 2016-01-01)
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Random attractors for stochastic lattice dynamical systems with infinite multiplicative white noiseRandom attractors for stochastic lattice dynamical systems with infinite multiplicative white noise

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Xiaoying, Han; Xiaoying, Han; Schmalfuss, Björn; Schmalfuss, Björn; Valero Cuadra, José; Valero Cuadra, José (2016-01-01)
In this paper we investigate the long term behavior of a stochastic lattice dynamical system with a diffusive nearest ...
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Impulsive neutral functional differential equations driven by a fractional Brownian motion with unbounded delayImpulsive neutral functional differential equations driven by a fractional Brownian motion with unbounded delay

Boudaoui, Ahmed; Boudaoui, Ahmed; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ouahab, Abdelghani; Ouahab, Abdelghani (Taylor & Francis, 2016-01-01)
In this paper, we prove the local and global existence and attractivity of mild solutions for stochastic impulsive neutral functional differential equations with infinite delay, driven by fractional Brownian motion.
Chapter of Book
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A random model for immune response to virus in fluctuating environmentsA random model for immune response to virus in fluctuating environments

Sadovnichiy, Victor A.; Sadovnichiy, Victor A.; Zgurovsky, Mikhail Z.; Zgurovsky, Mikhail Z.; Asai, Yusuke; Asai, Yusuke; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Han, Xiaoying; Han, Xiaoying; Kloeden, Peter E.; Kloeden, Peter E. (Springer, 2016-01-01)
In this work we study a model for virus dynamics with a random immune response and a random production rate of susceptible ...
Chapter of Book
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Some aspects concerning the dynamics of stochastic chemostatsSome aspects concerning the dynamics of stochastic chemostats

Sadovnichiy, Victor A.; Sadovnichiy, Victor A.; Zgurovsky, Mikhail Z.; Zgurovsky, Mikhail Z.; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; López de la Cruz, Javier; López de la Cruz, Javier (Springer, 2016-01-01)
In this paper we study a simple chemostat model influenced by white noise which makes this kind of models more realistic. ...
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A survey on impulsive dynamical systemsA survey on impulsive dynamical systems

Bonotto, Everaldo de Mello; Bonotto, Everaldo de Mello; Bortolan, Matheus Cheque; Bortolan, Matheus Cheque; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Collegari, Rodolfo; Collegari, Rodolfo (Bolyai Institute (University of Szeged), 2016-01-01)
In this survey we provide an introduction to the theory of impulsive dynamical systems in both the autonomous and nonautonomous ...
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New trends on nonlinear dynamics and its applicationsNew trends on nonlinear dynamics and its applications

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; García Guirao, Juan Luis; García Guirao, Juan Luis (American Institute of Mathematical Sciences, 2015-12-01)
This paper is the Preface of a special issue devoted to Nonlinear Dynamics and Complexity generated by the contributions ...
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Predation with indirect effects in fluctuating environmentsPredation with indirect effects in fluctuating environments

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato; Xiaoying, Han; Xiaoying, Han (Springer, 2015-06-30)
We investigate the long term dynamics for a predation model of Plankton community with indirect effects, under fluctuating ...
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Robustness of nonautonomous attractors for a family of nonlocal reaction–diffusion equations without uniquenessRobustness of nonautonomous attractors for a family of nonlocal reaction–diffusion equations without uniqueness

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Herrera Cobos, Marta; Herrera Cobos, Marta; Marín Rubio, Pedro; Marín Rubio, Pedro (Springer, 2015-06-17)
In this paper, we consider a non-autonomous nonlocal reactiondiffusion equation with a small perturbation in the nonlocal ...
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On the practical global uniform asymptotic stability of stochastic differential equationsOn the practical global uniform asymptotic stability of stochastic differential equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Hammami, Mohamed Ali; Hammami, Mohamed Ali; Mchiri, Lassaad; Mchiri, Lassaad (Taylor & Francis, 2015-06-04)
The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, ...
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Practical stability of stochastic delay evolution equationsPractical stability of stochastic delay evolution equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Hammami, Mohamed Ali; Hammami, Mohamed Ali; Mchiri, Lassaad; Mchiri, Lassaad (Springer, 2015-04-23)
In this paper we investigate the almost sure practical stability for a class of stochastic functional evolution equations. ...
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Chemostats with random inputs and wall growthChemostats with random inputs and wall growth

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Xiaoying, Han; Xiaoying, Han; Kloeden, Peter E.; Kloeden, Peter E. (John Wiley & Sons, 2015-03-12)
Chemostat refers to a laboratory device used for growing microorganisms in a cultured environment, and has been regarded ...
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On the stability of impulsive functional differential equations with infinite delaysOn the stability of impulsive functional differential equations with infinite delays

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Xiaodi, Li; Xiaodi, Li; Rakkiyappan, R.; Rakkiyappan, R.; Xiaoying, Han; Xiaoying, Han (2015-01-01)
In this paper, the stability problem of impulsive functional differential equations with infinite delays is considered. ...
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Long-time behavior of a non-autonomous parabolic equation with nonlocal diffusion and sublinear termsLong-time behavior of a non-autonomous parabolic equation with nonlocal diffusion and sublinear terms

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Herrera Cobos, Marta; Herrera Cobos, Marta; Marín Rubio, Pedro; Marín Rubio, Pedro (Pergamon Press, 2015-01-01)
This paper is devoted to study the asymptotic behavior of a time-dependent parabolic equation with nonlocal diffusion and ...
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Effects of additive and multiplicative noise on the dynamics of a parabolic equationEffects of additive and multiplicative noise on the dynamics of a parabolic equation

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato (Natural Sciences Publishing Corporation, 2015-01-01)
We consider the effects of additive and multiplicative noise on the asymptotic behavior of a fourth order parabolic equation ...
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Nonautonomous chemostats with variable delaysNonautonomous chemostats with variable delays

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Xiaoying, Han; Xiaoying, Han; Kloeden, Peter E.; Kloeden, Peter E. (Society for Industrial and Applied Mathematics, 2015-01-01)
The appearance of delay terms in a chemostat model can be fully justified since the future behavior of a dynamical system ...
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Dynamics of nonautonomous chemostat modelsDynamics of nonautonomous chemostat models

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Xiaoying, Han; Xiaoying, Han; Kloeden, Peter E.; Kloeden, Peter E.; Rapaport, Alain; Rapaport, Alain (2015-01-01)
Chemostat models have a long history in the biological sciences as well as in biomathematics. Hitherto most investigations ...
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Exponential behavior of solutions to stochastic integrodifferential equations with distributed delaysExponential behavior of solutions to stochastic integrodifferential equations with distributed delays

Diop, Mamadou Abdoul; Diop, Mamadou Abdoul; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ndiaye, Abdoul Aziz; Ndiaye, Abdoul Aziz (Taylor & Francis Inc., 2015-01-01)
In this work, we study the existence, uniqueness, and exponential asymptotic behavior of mild solutions to stochastic integrodifferential delay evolution equations. We assume that the non-delay part generates a C0-semigroup.
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Asymptotic stability of neutral stochastic functional integro-differential equations with impulsesAsymptotic stability of neutral stochastic functional integro-differential equations with impulses

Diop, Mamadou Abdoul; Diop, Mamadou Abdoul; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Institute of Mathematical Statistics, 2015-01-01)
This paper is concerned with the existence and asymptotic stability in the \,p-th moment of mild solutions of nonlinear ...
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Well--posedness and asymptotic behaviour for a non-classical and non-autonomous diffusion equation with delayWell--posedness and asymptotic behaviour for a non-classical and non-autonomous diffusion equation with delay

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Márquez Durán, Antonio Miguel; Márquez Durán, Antonio Miguel; Rivero Garvía, Luis Felipe; Rivero Garvía, Luis Felipe (2015-01-01)
In this paper, it is analyzed a non-classical non-autonomous di_usion equation with delay. First, the well-posedness and ...
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Attractors for non-autonomous retarded lattice dynamical systemsAttractors for non-autonomous retarded lattice dynamical systems

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Morillas Jurado, Francisco; Morillas Jurado, Francisco; Valero Cuadra, José; Valero Cuadra, José (De Gruyter Open, 2015-01-01)
In this paperwe study a non-autonomous lattice dynamical system with delay. Under rather general growth and dissipative ...
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Practical exponential stability in mean square of stochastic partial differential equationsPractical exponential stability in mean square of stochastic partial differential equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Hammami, Mohamed Ali; Hammami, Mohamed Ali; Mchiri, Lassaad; Mchiri, Lassaad (Springer - Verlag Italia Srl, 2015-01-01)
The main aim of this paper is to establish some criteria for the mean square and almost sure practical exponential stability of a nonlinear monotone stochastic partial differential equations.
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Chemostats with time-dependent inputs and wall growthChemostats with time-dependent inputs and wall growth

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Xiaoying, Han; Xiaoying, Han; Kloeden, Peter E.; Kloeden, Peter E. (Natural Sciences Publishing Corporation, 2015-01-01)
Traditional assumptions in the simple chemostat model include fixed availability of the nutrient and its supply rate, and ...
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A survey on Navier-Stokes models with delays: Existence, uniqueness and asymptotic behavior of solutionsA survey on Navier-Stokes models with delays: Existence, uniqueness and asymptotic behavior of solutions

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Xiaoying, Han; Xiaoying, Han (2015-01-01)
In this survey paper we review several aspects related to Navier-Stokes models when some hereditary characteristics ...
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Morse decomposition of global attractors with infinite componentsMorse decomposition of global attractors with infinite components

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Jara Pérez, Juan Carlos; Jara Pérez, Juan Carlos; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Valero Cuadra, José; Valero Cuadra, José (2015-01-01)
In this paper we describe some dynamical properties of a Morse decomposition with a countable number of sets. In particular, ...
PhD Thesis
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Caracterización de los atractores en sistemas dinámicos no autónomosCaracterización de los atractores en sistemas dinámicos no autónomos

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Jara Pérez, Juan Carlos; Jara Pérez, Juan Carlos (2014-03-21)
El estudio de los sistemas dinámicos es de gran importancia, ya que están relacionados con fenómenos del mundo real. Los ...
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Practical asymptotic stability of nonlinear stochastic evolution equationsPractical asymptotic stability of nonlinear stochastic evolution equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Hammami, Mohamed Ali; Hammami, Mohamed Ali; Mchiri, Lassaad; Mchiri, Lassaad (2014-01-01)
In this paper we establish some su cient conditions ensuring almost sure practical asymptotic stability with a non-exponential decay rate for solutions to stochastic evolution equations based on Lyapunov techniques.
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Pullback attractor for a non-linear evolution equation in elasticityPullback attractor for a non-linear evolution equation in elasticity

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato (2014-01-01)
We prove the existence of a pullback attractor for a non{autonomous fourth order evolution equation arising in the fi eld ...
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Fixed points and exponential stability for stochastic partial integro–differential equations with delaysFixed points and exponential stability for stochastic partial integro–differential equations with delays

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Diop, Mamadou Abdoul; Diop, Mamadou Abdoul; Ndoye, Ahmet Seyni; Ndoye, Ahmet Seyni (Research India Publications, 2014-01-01)
In this paper, we study the existence and asymptotic stability in the pth-moment of mild solutions of nonlinear impulsive ...
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Asymptotic Behaviour of a Non-Autonomous Lorenz-84 SystemAsymptotic Behaviour of a Non-Autonomous Lorenz-84 System

Anguiano Moreno, María; Anguiano Moreno, María; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (2014-01-01)
The so called Lorenz-84 model has been used in climatological studies, for example by coupling it with a low-dimensional ...
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On Differential Equations with Delay in Banach Spaces and Attractors for Retarded Lattice Dynamical SystemsOn Differential Equations with Delay in Banach Spaces and Attractors for Retarded Lattice Dynamical Systems

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Morillas Jurado, Francisco; Morillas Jurado, Francisco; Valero Cuadra, José; Valero Cuadra, José (2014-01-01)
In this paper we first prove a rather general theorem about existence of solutions for an abstract differential equation ...
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Existence results fortime-dependent neutral functional integrodifferential equations driven by a fractional Brownian motionExistence results fortime-dependent neutral functional integrodifferential equations driven by a fractional Brownian motion

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Diop, Mamadou Abdoul; Diop, Mamadou Abdoul; Ndiaye, Abdoul Aziz; Ndiaye, Abdoul Aziz (Euclidean Press, 2014-01-01)
This article presents some results on existence and uniqueness of mild solutions to neutral stochastic functional evolution ...
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Stability of delay evolution equations with stochastic perturbationsStability of delay evolution equations with stochastic perturbations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Shaikhet, Leonid; Shaikhet, Leonid (2014-01-01)
The investigation of stability for hereditary systems is often related to the construction of Lyapunov functionals. The ...
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Asymptotic Behaviour of a Logistic Lattice SystemAsymptotic Behaviour of a Logistic Lattice System

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Morillas Jurado, Francisco; Morillas Jurado, Francisco; Valero Cuadra, José; Valero Cuadra, José (2014-01-01)
In this paper we study the asymptotic behaviour of solutions of a lattice dynamical system of a logistic type. Namely, we ...
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Stability of stationary solutions to 2D-Navier-Stokes models with delaysStability of stationary solutions to 2D-Navier-Stokes models with delays

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Xiaoying, Han; Xiaoying, Han (International Press, 2014-01-01)
In this paper we establish some sufficient conditions for the exponential stability of the stationary solution to a ...
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Asymptotic behavior of neutral stochastic partial functional integro-differential equations driven by a fractional Brownian motionAsymptotic behavior of neutral stochastic partial functional integro-differential equations driven by a fractional Brownian motion

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Diop, Mamadou Abdoul; Diop, Mamadou Abdoul; Ndiaye, Abdoul Aziz; Ndiaye, Abdoul Aziz (2014-01-01)
This paper deals with the existence, uniqueness and asymptotic behavior of mild solutions to neutral stochastic delay ...
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Attractivity for Neutral Functional Differential EquationsAttractivity for Neutral Functional Differential Equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kiss, Gábor; Kiss, Gábor (2013-01-01)
We study the long term dynamics of non-autonomous functional di fferential equations. Namely, we establish existence results ...
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Random attractors for stochastic 2D-Navier-Stokes equations in some unbounded domainsRandom attractors for stochastic 2D-Navier-Stokes equations in some unbounded domains

Brzezniak, Zdzislaw; Brzezniak, Zdzislaw; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Li, Yuhong; Li, Yuhong; Lukaszewicz, Grzegorz; Lukaszewicz, Grzegorz; Real Anguas, José; Real Anguas, José (2013-01-01)
We show that the stochastic flow generated by the 2-dimensional Stochastic Navier-Stokes equations with rough noise on a ...
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Non-autonomous morse-decomposition and Lyapunov functions for gradient-like processesNon-autonomous morse-decomposition and Lyapunov functions for gradient-like processes

Aragão Costa, Eder Ritis; Aragão Costa, Eder Ritis; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Carvalho, Alexandre Nolasco; Carvalho, Alexandre Nolasco; Langa Rosado, José Antonio; Langa Rosado, José Antonio (2013-01-01)
We define (time dependent) Morse-decompositions for non-autonomous evolution processes (non-autonomous dynamical systems) ...
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Skew Product Semiflows and Morse DecompositionSkew Product Semiflows and Morse Decomposition

Bortolan, Matheus Cheque; Bortolan, Matheus Cheque; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Carvalho, Alexandre Nolasco; Carvalho, Alexandre Nolasco; Langa Rosado, José Antonio; Langa Rosado, José Antonio (2013-01-01)
This paper is devoted to the investigation of the dynamics of non-autonomous differential equations. The description of ...
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Existence, uniqueness and asymptotic behavior of solutions for a nonclassical diffusion equation with delayExistence, uniqueness and asymptotic behavior of solutions for a nonclassical diffusion equation with delay

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Márquez Durán, Antonio Miguel; Márquez Durán, Antonio Miguel (2013-01-01)
A nonclassical nonautonomous diffusion equation with delay is analyzed. First, we prove the existence and uniqueness of ...
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On the Structure of the Global Attractor for Infinite-Dimensional Non-Autonomous Dynamical Systems with Weak ConvergenceOn the Structure of the Global Attractor for Infinite-Dimensional Non-Autonomous Dynamical Systems with Weak Convergence

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Cheban, David; Cheban, David (2013-01-01)
The aim of this paper is to describe the structure of global attractors for infinite-dimensional non-autonomous dynamical ...
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Pullback attractors for a non-autonomous integro-differential equation with memory in some unbounded domainsPullback attractors for a non-autonomous integro-differential equation with memory in some unbounded domains

Anguiano Moreno, María; Anguiano Moreno, María; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José (2013-01-01)
The main aim of this paper is to analyse the asymptotic behaviour of a non-autonomous integrodifferential parabolic equation ...
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Neutral stochastic delay partial functional integro-differential equations driven by a fractional Brownian motionNeutral stochastic delay partial functional integro-differential equations driven by a fractional Brownian motion

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Diop, Mamadou Abdoul; Diop, Mamadou Abdoul (2013-01-01)
This paper deals with the existence and uniqueness of mild solutions to neutral stochastic delay functional integro-di ...
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Pullback attractors for differential equations with multiple variable delays in Lipschitz nonlinearitiesPullback attractors for differential equations with multiple variable delays in Lipschitz nonlinearities

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kiss, Gábor; Kiss, Gábor; Taniguchi, Takeshi; Taniguchi, Takeshi (2013-01-01)
We establish the results on the existence of pullback attractors for nonautonomous functional differential equations with ...
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The three dimensional globally modified Navier-Stokes equations: Recent developmentsThe three dimensional globally modified Navier-Stokes equations: Recent developments

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E. (2013-01-01)
The globally modified Navier-Stokes equations (GMNSE) were introduced by Caraballo, Kloeden & Real in 2006 and have been ...
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Attractors of stochastic lattice dynamical systems with a multiplicative noise and non-Lipschitz nonlinearitiesAttractors of stochastic lattice dynamical systems with a multiplicative noise and non-Lipschitz nonlinearities

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Morillas, F.; Morillas, F.; Valero, J.; Valero, J. (Elsevier, 2012-04-16)
In this paper we study the asymptotic behavior of solutions of a first-order stochastic lattice dynamical system with a ...
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An Estimate On the Fractal Dimension of Attractors of Gradient-Like Dynamical SystemsAn Estimate On the Fractal Dimension of Attractors of Gradient-Like Dynamical Systems

Bortolan, Matheus Cheque; Bortolan, Matheus Cheque; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Carvalho, Alexandre Nolasco; Carvalho, Alexandre Nolasco; Langa Rosado, José Antonio; Langa Rosado, José Antonio (2012-01-01)
This paper is dedicated to estimate the fractal dimension of exponential global attractors of some generalized gradient-like ...
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Random attractors for stochastic lattice systems with non-Lipschitz non-linearityRandom attractors for stochastic lattice systems with non-Lipschitz non-linearity

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Morillas Jurado, Francisco; Morillas Jurado, Francisco; Valero Cuadra, José; Valero Cuadra, José (2012-01-01)
In this paper we study the asymptotic behaviour of solutions of a first-order stochastic lattice dynamical system with an ...
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Gradient Infinite-Dimensional Random Dynamical SystemsGradient Infinite-Dimensional Random Dynamical Systems

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Liu, Zenxhin; Liu, Zenxhin (2012-01-01)
In this paper we introduce the concept of a gradient random dynamical system as a random semiflow possessing a continuous ...
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Continuity of Lyapunov Functions and of Energy Level for a Generalized Gradient SemigroupContinuity of Lyapunov Functions and of Energy Level for a Generalized Gradient Semigroup

Aragão Costa, Eder Ritis; Aragão Costa, Eder Ritis; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Carvalho, Alexandre Nolasco; Carvalho, Alexandre Nolasco; Langa Rosado, José Antonio; Langa Rosado, José Antonio (2012-01-01)
The global attractor of a gradient-like semigroup has a Morse decomposition. Associated to this Morse decomposition there ...
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PhD Thesis
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Attractors for nonlinear and non-autonomous parabolic PDES in unbounded domainsAttractors for nonlinear and non-autonomous parabolic PDES in unbounded domains

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José; Valero Cuadra, José; Valero Cuadra, José; Anguiano Moreno, María; Anguiano Moreno, María (2011-09-01)
Este trabajo está dividido en cinco capítulos. En los Capítulos 1 y 3, se trata la parte teórica de los sistemas dinámicos ...
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On the asymptotic behaviour of a stochastic 3D Lans-Alpha modelOn the asymptotic behaviour of a stochastic 3D Lans-Alpha model

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Márquez Durán, Antonio Miguel; Márquez Durán, Antonio Miguel; Real Anguas, José; Real Anguas, José (2011-01-01)
The long-time behaviour of a stochastic 3D LANS-® model on a bounded domain is analysed. First, we reformulate the model ...
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A Non-Autonomous Strongly Damped Wave Equation: Existence and Continuity of the Pullback AttractorA Non-Autonomous Strongly Damped Wave Equation: Existence and Continuity of the Pullback Attractor

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Carvalho, Alexandre Nolasco; Carvalho, Alexandre Nolasco; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Rivero Garvía, Luis Felipe; Rivero Garvía, Luis Felipe (2011-01-01)
In this paper we consider the strongly damped wave equation with time dependent terms utt − u − γ(t) ut + β"(t)ut = f(u), ...
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Stability of Gradient Semigroups Under PerturbationsStability of Gradient Semigroups Under Perturbations

Aragão Costa, Eder Ritis; Aragão Costa, Eder Ritis; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Carvalho, Alexandre Nolasco; Carvalho, Alexandre Nolasco; Langa Rosado, José Antonio; Langa Rosado, José Antonio (2011-01-01)
In this paper we prove that gradient-like semigroups (in the sense of Carvalho and Langa (2009 J. Diff. Eqns 246 2646–68)) ...
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Almost Periodic and Asymptotically Almost Periodic Solutions of Liénard EquationsAlmost Periodic and Asymptotically Almost Periodic Solutions of Liénard Equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Cheban, David; Cheban, David (2011-01-01)
The aim of this paper is to study the almost periodic and asymptotically almost periodic solutions on (0,+1) of the Li´enard ...
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The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional brownian motionThe existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional brownian motion

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; Taniguchi, Takeshi; Taniguchi, Takeshi (2011-01-01)
In this paper we investigate the existence, uniqueness and exponential asymptotic behavior of mild solutions to stochastic ...
PhD Thesis
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Atractores pullback existencia y estructura para una ecuación de ondas con amortiguamiento no autónomoAtractores pullback existencia y estructura para una ecuación de ondas con amortiguamiento no autónomo

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Rivero Garvía, Luis Felipe; Rivero Garvía, Luis Felipe (2011-01-01)
Este trabajo está dividido en dos partes. Una primera en la que se trata la parte teórica de los sistemas dinámicos autónomos ...
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Three dimensional system of globally modified navier-Stokes equation with delayThree dimensional system of globally modified navier-Stokes equation with delay

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real, José; Real, José; Márquez, Antonio M.; Márquez, Antonio M. (2010-09-04)
We prove the existence and uniqueness of strong solutions of a three-dimensional system of glob-ally modified Navier–Stokes ...
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Existence of Pullback Attractors for Pullback Asymptotically Compact ProcessesExistence of Pullback Attractors for Pullback Asymptotically Compact Processes

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Carvalho, Alexandre Nolasco; Carvalho, Alexandre Nolasco; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Rivero Garvía, Luis Felipe; Rivero Garvía, Luis Felipe (2010-01-01)
This paper is concerned with the existence of pullback attractors for evolution processes. Our aim is to provide results ...
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Recent developments in dynamical systems: three perspectivesRecent developments in dynamical systems: three perspectives

Balibrea Gallego, Francisco; Balibrea Gallego, Francisco; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E.; Valero Cuadra, José; Valero Cuadra, José (2010-01-01)
This paper aims to an present account of some problems considered in the past years in Dynamical Systems, new research directions and also provide some open problems.
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Almost periodic and almost automorphic solutions of linear differential equationsAlmost periodic and almost automorphic solutions of linear differential equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Cheban, David; Cheban, David (2010-01-01)
We analyze the existence of almost periodic (respectively, almost automorphic, recurrent) solutions of a linear non-homogeneous ...
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Three-dimensional system of globally modified Navier-Stokes equations with delayThree-dimensional system of globally modified Navier-Stokes equations with delay

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José; Márquez, Antonio M.; Márquez, Antonio M. (2010-01-01)
We prove the existence and uniqueness of strong solutions of a three-dimensional system of globally modified Navier–Stokes ...
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Asymptotic behaviour of a stochastic semilinear dissipative functional equation without uniqueness of solutionsAsymptotic behaviour of a stochastic semilinear dissipative functional equation without uniqueness of solutions

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; Schmalfuss, Björn; Schmalfuss, Björn; Valero Cuadra, José; Valero Cuadra, José (2010-01-01)
In this work we present the existence and uniqueness of pullback and random attractors for stochastic evolution equations ...
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H2-boundedness of the pullback attractor for a non-nutonomous reaction-diffusion equationH2-boundedness of the pullback attractor for a non-nutonomous reaction-diffusion equation

Anguiano Moreno, María; Anguiano Moreno, María; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José (2010-01-01)
We prove some regularity results for the pullback attractor of a reaction-diffusion model. First we establish a general ...
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Pullback attractors for reaction-diffusion equations in some unbounded domains with an H-1 -valued non-autonomous forcing term and without uniqueness of solutionsPullback attractors for reaction-diffusion equations in some unbounded domains with an H-1 -valued non-autonomous forcing term and without uniqueness of solutions

Anguiano Moreno, María; Anguiano Moreno, María; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José; Valero Cuadra, José; Valero Cuadra, José (2010-01-01)
The existence of a pullback attractor for a reaction-diffusion equations in an unbounded domain containing a non-autonomous ...
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Global attractor for a non-autonomous integro-differential equation in materials with memoryGlobal attractor for a non-autonomous integro-differential equation in materials with memory

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; Schmalfuss, Björn; Schmalfuss, Björn; Valero Cuadra, José; Valero Cuadra, José (2010-01-01)
The long-time behavior of an integro-differential parabolic equation of diffusion type with memory terms, expressed by ...
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Non-Autonomous Attractor for Integro-Differential Evolution EquationsNon-Autonomous Attractor for Integro-Differential Evolution Equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E. (2009-01-01)
We show that infinite-dimensional integro-differential equations which involve an integral of the solution over the time ...
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A gradient-like non autonomous evolution processA gradient-like non autonomous evolution process

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Rivero Garvía, Luis Felipe; Rivero Garvía, Luis Felipe; Carvalho, Alexandre Nolasco; Carvalho, Alexandre Nolasco (2009-01-01)
In this paper we consider a dissipative damped wave equation with non-autonomous damping of the form utt + ¯(t)ut = ¢u + ...
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Attractors for Differential Equations with Multiple Variable DelaysAttractors for Differential Equations with Multiple Variable Delays

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kiss, Gábor; Kiss, Gábor (2009-01-01)
We establish some results on the existence of pullback attractors for non-autonomous delay di fferential equations with ...
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Asymptotic Behaviour of the Three-Dimensional Á-Navier-Stokes Model with Locally Lipschitz Delay Forcing TermsAsymptotic Behaviour of the Three-Dimensional Á-Navier-Stokes Model with Locally Lipschitz Delay Forcing Terms

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Márquez Durán, Antonio Miguel; Márquez Durán, Antonio Miguel; Real Anguas, José; Real Anguas, José (2009-01-01)
We obtain some results on the existence and uniqueness, and exponential stability of solutions for the three-dimensional ...
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Almost periodic and almost automorphic solutions of linear differential/difference equations without Favard's separation condition. IAlmost periodic and almost automorphic solutions of linear differential/difference equations without Favard's separation condition. I

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Cheban, David; Cheban, David (2009-01-01)
The well-known Favard's theorem states that the linear differential equation x′=A(t)x+f(t) Turn MathJax on with Bohr ...
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Almost periodic and almost automorphic solutions of linear differential/difference equations without Favard's separation condition. IIAlmost periodic and almost automorphic solutions of linear differential/difference equations without Favard's separation condition. II

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Cheban, David; Cheban, David (2009-01-01)
In this paper we continue the research started in a previous paper, where we proved that the linear differential equation (1) ...
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Non-autonomous and random attractors for delay random semilinear equations without uniquenessNon-autonomous and random attractors for delay random semilinear equations without uniqueness

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; Schmalfuss, Björn; Schmalfuss, Björn; Valero Cuadra, José; Valero Cuadra, José (2008-01-01)
We first prove the existence and uniqueness of pullback and random attractors for abstract multi-valued non-autonomous and ...
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Synchronization of Systems with Multiplicative NoiseSynchronization of Systems with Multiplicative Noise

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E.; Neuenkirch, Andreas; Neuenkirch, Andreas (2008-01-01)
The synchronization of Stratonovich stochastic di erential equations (SDE) with a one-sided dissipative Lipschitz drift ...
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Pullback Attractors for Stochastic Heat Equations in Materials with MemoryPullback Attractors for Stochastic Heat Equations in Materials with Memory

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Chueshov, Igor D.; Chueshov, Igor D.; Real Anguas, José; Real Anguas, José (2008-01-01)
We study the asymptotic behaviour of a non-autonomous stochastic reaction-diffusion equation with memory. In fact, we prove ...
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Attractors for Stochastic Lattice Dynamical Systems with a Multiplicative NoiseAttractors for Stochastic Lattice Dynamical Systems with a Multiplicative Noise

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Lu, Kening; Lu, Kening (2008-01-01)
In this paper, we consider a stochastic lattice di®erential equation with di®usive nearest neighbor interaction, a dissipative ...
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Invariant Measures and Statistical Solutions of the Globally Modified Navier-Stokes EquationsInvariant Measures and Statistical Solutions of the Globally Modified Navier-Stokes Equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E.; Real Anguas, José; Real Anguas, José (2008-01-01)
We obtain regularity results for solutions of the three dimensional system of globally modified Navier-Stokes equations, ...
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Stabilisation of differential inclusions and PDEs without uniqueness by noiseStabilisation of differential inclusions and PDEs without uniqueness by noise

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Valero Cuadra, José; Valero Cuadra, José (2008-01-01)
We prove that the asymptotic behaviour of partial differential inclusions and partial differential equations without ...
Presentation
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Sobre la existencia de atractores para ecuaciones aleatorias de reacción-difusión con retardosSobre la existencia de atractores para ecuaciones aleatorias de reacción-difusión con retardos

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; Schmalfuss, Björn; Schmalfuss, Björn; Valero Cuadra, José; Valero Cuadra, José (2007-09-01)
En primer lugar probamos la existencia y unicidad de atractor para sistemas dinámicos multivaluados abstractos, tanto en ...
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Numerical and finite delay approximations of attractors for logistic differential-integral equations with infinite delayNumerical and finite delay approximations of attractors for logistic differential-integral equations with infinite delay

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E.; Marín Rubio, Pedro; Marín Rubio, Pedro (2007-01-01)
The upper semi-continuous convergence of approximate attractors for an infinite delay differential equation of logistic ...
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Attractors for differential equations with unbounded delaysAttractors for differential equations with unbounded delays

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Marín Rubio, Pedro; Marín Rubio, Pedro; Valero Cuadra, José; Valero Cuadra, José (Elsevier, 2007-01-01)
We prove the existence of attractors for some types of differential problems containing infinite delays. Applications and ...
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Method of Lyapunov Functionals Construction in Stability of Delay Evolution EquationsMethod of Lyapunov Functionals Construction in Stability of Delay Evolution Equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José; Shaikhet, Leonid; Shaikhet, Leonid (2007-01-01)
Stability investigation of hereditary systems often is connected with the construction of Lyapunov functionals. The general ...
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Existence and Asymptotic Behaviour for Stochastic Heat Equations with Multiplicative Noise in Materials With MemoryExistence and Asymptotic Behaviour for Stochastic Heat Equations with Multiplicative Noise in Materials With Memory

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Chueshov, Igor D.; Chueshov, Igor D.; Marín Rubio, Pedro; Marín Rubio, Pedro; Real Anguas, José; Real Anguas, José (2007-01-01)
The existence and uniqueness of solutions for a stochastic reaction-diffusion equation with infinite delay is proved. ...
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Existence of exponentially attracting stationary solutions for delay evolution equationsExistence of exponentially attracting stationary solutions for delay evolution equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; Schmalfuss, Björn; Schmalfuss, Björn (2007-01-01)
We consider the exponential stability of semilinear stochastic evolution equations with delays when zero is not a solution ...
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Levitan/Bohr Almost Periodic and Almost Automorphic Solutions of Second-Order Monotone Differential EquationsLevitan/Bohr Almost Periodic and Almost Automorphic Solutions of Second-Order Monotone Differential Equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Cheban, David; Cheban, David (2007-01-01)
The aim of this paper is to prove the existence of Levitan/Bohr almost periodic, almost automorphic, recurrent and Poisson ...
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The Exponential Stability of Neutral Stochastic Delay Partial Differential EquationsThe Exponential Stability of Neutral Stochastic Delay Partial Differential Equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José; Taniguchi, Takeshi; Taniguchi, Takeshi (2007-01-01)
In this paper we analyse the almost sure exponential stability and ultimate boundedness of the solutions to a class of ...
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Synchronization of a Stochastic Reaction-Diffusion System On a Thin Two-Layer DomainSynchronization of a Stochastic Reaction-Diffusion System On a Thin Two-Layer Domain

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Chueshov, Igor D.; Chueshov, Igor D.; Kloeden, Peter E.; Kloeden, Peter E. (2007-01-01)
A system of semilinear parabolic stochastic partial differential equations with additive space-time noise is considered ...
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Recent results on stabilization of PDEs by noiseRecent results on stabilization of PDEs by noise

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Sociedad Española de Matemática Aplicada, 2006-12-01)
This paper is intended to be a brief review on some recent results on the stabilization effect produced by noise in phenomena ...
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Discretization of Asymptotically Stable Stationary Solutions of Delay Differential Equations with a Random Stationary DelayDiscretization of Asymptotically Stable Stationary Solutions of Delay Differential Equations with a Random Stationary Delay

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E.; Real Anguas, José; Real Anguas, José (2006-01-01)
We prove the existence of a stationary random solution to a delay random ordinary differential system which attracts all ...
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Comparison of the long-time behaviour of linear Ito and Stratonovich partial differential equationsComparison of the long-time behaviour of linear Ito and Stratonovich partial differential equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio (2006-01-01)
In this paper, we point out the different long-time behaviour of stochastic partial differential equations when one considers ...
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Pullback and forward attractors for a 3D Lans-alpha model with delayPullback and forward attractors for a 3D Lans-alpha model with delay

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Márquez Durán, Antonio Miguel; Márquez Durán, Antonio Miguel; Real Anguas, José; Real Anguas, José (2006-01-01)
We analyse the asymptotic behaviour of a 3D Lagrangian averaged Navier-Stokes -model (3D LANS) with delays. In fact, we ...
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Global and Pullback Attractors of Set-Valued Skew Product FlowsGlobal and Pullback Attractors of Set-Valued Skew Product Flows

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E.; Marín Rubio, Pedro; Marín Rubio, Pedro (2006-01-01)
We investigate the asymptotic behaviour of a general set-valued skew product flow (SVSPF), that is, a set-valued cocycle ...
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The effect of noise on the chafee-infante equation: a nonlinear case studyThe effect of noise on the chafee-infante equation: a nonlinear case study

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Crauel, Hans; Crauel, Hans; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Robinson, James C.; Robinson, James C. (2006-01-01)
We investigate the effect of perturbing the Chafee-Infante scalar reaction diffusion equation, ut−Δu = βu−u3, by noise. ...
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The pathwise numerical approximation of stationary solutions of semilinear stochastic evolution equationsThe pathwise numerical approximation of stationary solutions of semilinear stochastic evolution equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E. (2006-01-01)
Under a one-sided dissipative Lipschitz condition on its drift, a stochastic evolution equation with additive noise of the ...
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Pullback attractors for asymptotically compact non-autonomous dynamical systemsPullback attractors for asymptotically compact non-autonomous dynamical systems

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Lukaszewicz, Grzegorz; Lukaszewicz, Grzegorz; Real Anguas, José; Real Anguas, José (2006-01-01)
First, we introduce the concept of pullback asymptotically compact non-autonomous dynamical system as an extension of the ...
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Pullback attractors for non-autonomous 2D-Navier-Stokes equations in some unbounded domainsPullback attractors for non-autonomous 2D-Navier-Stokes equations in some unbounded domains

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Lukaszewicz, Grzegorz; Lukaszewicz, Grzegorz; Real Anguas, José; Real Anguas, José (2006-01-01)
In this Note we first introduce the concept of pullback asymptotic compactness. Next, we establish a result ensuring the ...
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Stabilization of Stationary Solutions of Evolution Equations by NoiseStabilization of Stationary Solutions of Evolution Equations by Noise

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E.; Schmalfuss, Björn; Schmalfuss, Björn (2006-01-01)
We investigate the existence, uniqueness and exponential stability of non-constant stationary solutions of stochastic ...
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Stability of Nonlinear Functional Stochastic Evolution Equations of Second Order in TimeStability of Nonlinear Functional Stochastic Evolution Equations of Second Order in Time

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; Real Anguas, José; Real Anguas, José (2006-01-01)
Sufficient conditions for exponential mean square stability of solutions to delayed stochastic partial differential equations ...
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On the existence and uniqueness of solutions to stochastic three-dimensional Lagrangian averaged Navier-Stokes equationsOn the existence and uniqueness of solutions to stochastic three-dimensional Lagrangian averaged Navier-Stokes equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José; Taniguchi, Takeshi; Taniguchi, Takeshi (2006-01-01)
We prove existence and uniqueness of solutions for a stochastic version of the 3DLagrangian averaged Navier-Stokes (LANS-®) ...
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Addendum To "Global Attractors for Multivalued Random Dynamical Systems'' [Nonlinear Analysis 48(2002) 805-829]Addendum To "Global Attractors for Multivalued Random Dynamical Systems'' [Nonlinear Analysis 48(2002) 805-829]

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Valero Cuadra, José; Valero Cuadra, José (2005-01-01)
The aim of this note is to clarify a misleading statement which appeared in our fi rst paper dealing with the concept of global random attractor for multivalued random dynamical systems, as well as in the subsequent work
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Asymptotic Behaviour of Monotone Multi-Valued Dynamical SystemsAsymptotic Behaviour of Monotone Multi-Valued Dynamical Systems

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Valero Cuadra, José; Valero Cuadra, José (2005-01-01)
We introduce the concept of a monotone multi-valued semi- ow as an order-preserving map. This de nition is motivated by ...
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Existence of invariant manifolds for coupled parabolic and hyperbolic stochastic partial differential equationsExistence of invariant manifolds for coupled parabolic and hyperbolic stochastic partial differential equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Chueshov, Igor D.; Chueshov, Igor D.; Langa Rosado, José Antonio; Langa Rosado, José Antonio (2005-01-01)
An abstract system of coupled nonlinear parabolic-hyperbolic partial differential equations subjected to additive white ...
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On the stochastic 3D-Lagrangian averaged Navier-Stokes Alpha-Model with finite delayOn the stochastic 3D-Lagrangian averaged Navier-Stokes Alpha-Model with finite delay

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Márquez Durán, Antonio Miguel; Márquez Durán, Antonio Miguel; Real Anguas, José; Real Anguas, José (2005-01-01)
Existence and uniqueness of solutions for a stochastic version of the 3D-Lagrangian averaged Navier-Stokes (LANS-®) equation in a bounded domain and containing some hereditary characteristics are proved.
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Autonomous and non-autonomous attractors for differential equations with delaysAutonomous and non-autonomous attractors for differential equations with delays

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Marín Rubio, Pedro; Marín Rubio, Pedro; Valero Cuadra, José; Valero Cuadra, José (2005-01-01)
The asymptotic behaviour of some types of retarded differential equations, with both variable and distributed delays, is ...
PhD Thesis
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Contribución al estudio de algunos modelos regidos por ecuaciones de evolución no autónomas y/o estocásticasContribución al estudio de algunos modelos regidos por ecuaciones de evolución no autónomas y/o estocásticas

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José; Márquez Durán, Antonio Miguel; Márquez Durán, Antonio Miguel (2005-01-01)
"Como es bien conocido, las ecuaciones de Navier-Stokes gobiernan el movimiento de fluidos comunes como el agua, el aire, ...
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The persistence of synchronization under environmental noiseThe persistence of synchronization under environmental noise

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E. (2005-01-01)
It is shown that the synchronization of dissipative systems persists when they are disturbed by additive noise no matter ...
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Attractors for 2D-Navier-Stokes models with delaysAttractors for 2D-Navier-Stokes models with delays

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José (2004-01-01)
The existence of an attractor for a 2D-Navier-Stokes system with delay is proved. The theory of pullback attractors is ...
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Exponentially Stable Stationary Solutions for Stochastic Evolution Equations and Their PerturbationExponentially Stable Stationary Solutions for Stochastic Evolution Equations and Their Perturbation

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E.; Schmalfuss, Björn; Schmalfuss, Björn (2004-01-01)
We consider the exponential stability of stochastic evolution equations with Lipschitz continuous non-linearities when ...
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Stabilisation of linear PDEs by Stratonovich noiseStabilisation of linear PDEs by Stratonovich noise

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Robinson, James C.; Robinson, James C. (2004-01-01)
Some results concerning the stability and stabilisation of stochastic linear partial differential equations in the sense ...
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Pullback and Forward Attractors for a Damped Wave Equation with DelaysPullback and Forward Attractors for a Damped Wave Equation with Delays

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E.; Real Anguas, José; Real Anguas, José (2004-01-01)
The existence of a pullback (and also a uniform forward) attractor is proved for a damped wave equation containing a delay ...
PhD Thesis
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Existencia, unicidad y comportamiento asintótico en algunos sistemas dinámicos deterministas y estocásticosExistencia, unicidad y comportamiento asintótico en algunos sistemas dinámicos deterministas y estocásticos

Real Anguas, José; Real Anguas, José; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Marín Rubio, Pedro; Marín Rubio, Pedro (2003-05-23)
La memoria está compuesta de dos partes: la primera se enmarca dentro del Análisis Estocástico y la segunda parte en la ...
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Asymptotic Behaviour of 2D-Navier-Stokes Equations with DelaysAsymptotic Behaviour of 2D-Navier-Stokes Equations with Delays

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José (2003-01-01)
Some results on the asymptotic behaviour of solutions to Navier-Stokes equations when the external force contains some ...
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Asymptotic stability of nonlinear stochastic evolution equationsAsymptotic stability of nonlinear stochastic evolution equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; Real Anguas, José; Real Anguas, José (2003-01-01)
Some results on the pathwise asymptotic stability of solutions to stochastic partial differential equations are proved. ...
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On the relationship between solutions of stochastic and random differential inclusionsOn the relationship between solutions of stochastic and random differential inclusions

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Valero Cuadra, José; Valero Cuadra, José (2003-01-01)
Some results on the relationship of the solutions of a stochastic di erential inclusion and the corresponding random di ...
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The dimension of attractors of nonautonomous partial differential equationsThe dimension of attractors of nonautonomous partial differential equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Valero Cuadra, José; Valero Cuadra, José (2003-01-01)
The concept of nonautonomous (or cocycle) attractor has become a proper tool for the study of the asymptotic behaviour of ...
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A Comparison Between Two Theories for Multi-Valued Semiflows and Their Asymptotic BehaviourA Comparison Between Two Theories for Multi-Valued Semiflows and Their Asymptotic Behaviour

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Marín Rubio, Pedro; Marín Rubio, Pedro; Robinson, James C.; Robinson, James C. (2003-01-01)
This paper presents a comparison between two abstract frameworks in which one can treat multi-valued semiflows and their ...
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The exponential behaviour of nonlinear stochastic functional equations of second order in timeThe exponential behaviour of nonlinear stochastic functional equations of second order in time

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; Real Anguas, José; Real Anguas, José (2003-01-01)
Sufficient conditions for exponential mean square stability of solutions to delayed stochastic partial differential equations ...
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Weak pullback attractors of setvalued processesWeak pullback attractors of setvalued processes

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E.; Marín Rubio, Pedro; Marín Rubio, Pedro (2003-01-01)
Weak pullback attractors are de ned for nonautonomous setvalued processes and their existence and upper semi continuous ...
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Pullback attractors of nonautonomous and stochastic multivalued dynamical systemsPullback attractors of nonautonomous and stochastic multivalued dynamical systems

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Melnik, Valery S.; Melnik, Valery S.; Valero Cuadra, José; Valero Cuadra, José (2003-01-01)
In this paper we study the existence of pullback global attractors for multivalued processes generated by differential ...
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Stochastic stabilization of differential systems with general decay rateStochastic stabilization of differential systems with general decay rate

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; Real Anguas, José; Real Anguas, José (2003-01-01)
Some sufficient conditions concerning stability of solutions of stochastic differential evolution equations with general ...
PhD Thesis
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Algunos resultados de existencia, unicidad y estabilidad para EDP funcionales estocásticas no linealesAlgunos resultados de existencia, unicidad y estabilidad para EDP funcionales estocásticas no lineales

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José; Garrido Atienza, María José; Garrido Atienza, María José (2002-01-01)
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The Exponential Behaviour and Stabilizability of Stochastic 2D-Navier-Stokes EquationsThe Exponential Behaviour and Stabilizability of Stochastic 2D-Navier-Stokes Equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Taniguchi, Takeshi; Taniguchi, Takeshi (2002-01-01)
Some results on the pathwise exponential stability of the weak solutions to a stochastic 2D-Navier-Stokes equation are ...
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Existence and uniqueness of solutions for delay stochastic evolution equationsExistence and uniqueness of solutions for delay stochastic evolution equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; Real Anguas, José; Real Anguas, José (2002-01-01)
Some results on the existence and uniqueness of solutions for stochastic evolution equations containing some hereditary ...
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Global Attractors for Multivalued Random Dynamical SystemsGlobal Attractors for Multivalued Random Dynamical Systems

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Valero Cuadra, José; Valero Cuadra, José (2002-01-01)
We introduce the concept of multivalued random dynamical system (MRDS) as a measurable multivalued flow satisfying the ...
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On the decay rate of solutions of non-autonomous differential systemsOn the decay rate of solutions of non-autonomous differential systems

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (2001-01-01)
Some results on the asymptotic behaviour of solutions of diff erential equations concerning general decay rate are proved. ...
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Global attractors for multivalued random dynamical systems generated by random differential inclusions with multiplicative noiseGlobal attractors for multivalued random dynamical systems generated by random differential inclusions with multiplicative noise

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Cuadra Valero, José; Cuadra Valero, José (2001-01-01)
In this paper we consider a stochastic differential inclusion with multiplicative noise. It is shown that it generates a multivalued random dynamical system for which there also exists a global random attractor.
Presentation
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Approximation of attractors for multivalued random dynamical systemsApproximation of attractors for multivalued random dynamical systems

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Valero Cuadra, José; Valero Cuadra, José (Masaryk University, 2001-01-01)
The concept of global attractor for stochastic partial differential inclusions has been recently introduced as a joint ...
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Navier-Stokes Equations with DelaysNavier-Stokes Equations with Delays

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José (2001-01-01)
Some results on the existence and uniqueness of solutions to Navier-Stokes equations when the external force contains some hereditary characteristics are proved.
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Global attractors for multivalued random semiflows generated by random differential inclusions with additive noiseGlobal attractors for multivalued random semiflows generated by random differential inclusions with additive noise

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Valero Cuadra, José; Valero Cuadra, José (2001-01-01)
We introduce the concept of multivalued random dynamical system (MRDS) as a measurable multivalued flow satisfying the ...
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On Stabilization of Partial Differential Equations by NoiseOn Stabilization of Partial Differential Equations by Noise

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Liu, Kai; Liu, Kai; Mao, Xuerong; Mao, Xuerong (2001-01-01)
Some results on stabilization of (deterministic and stochastic) partial differential equations are established. In particular, ...
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A Stochastic Pitchfork Bifurcation in a Reaction-Diffusion EquationA Stochastic Pitchfork Bifurcation in a Reaction-Diffusion Equation

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Robinson, James C.; Robinson, James C. (2001-01-01)
We study in some detail the structure of the random attractor for the Chafee{Infante reaction{di¬usion equation perturbed ...
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Attractors for differential equations with variable delaysAttractors for differential equations with variable delays

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Robinson, James C.; Robinson, James C. (2001-01-01)
Using the relatively new concept of a pullback attractor, we present some results on the existence of attractors for differential equations with variable delay. We give a variety of examples to which our result applies.
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Nonlinear Partial Functional Differential Equations: Existence and StabilityNonlinear Partial Functional Differential Equations: Existence and Stability

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (2001-01-01)
Existence and uniqueness of solutions for a class of nonlinear functional differential equations in Hilbert spaces are ...
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Asymptotic exponential stability for diffusion processes driven by stochastic differential equations in duals of nuclear spacesAsymptotic exponential stability for diffusion processes driven by stochastic differential equations in duals of nuclear spaces

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Liu, Kai; Liu, Kai (2001-01-01)
The main objective of this paper is to investigate the asymptotic stability for diffusion processes driven by a class of ...
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An exponential growth condition in H^2 for the pullback attractor of a non-autonomous reaction-diffusion equationAn exponential growth condition in H^2 for the pullback attractor of a non-autonomous reaction-diffusion equation

Anguiano Moreno, María; Anguiano Moreno, María; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José (2001-01-01)
Some exponential growth results for the pullback attractor of a reaction-diffusion when time goes to ¡1 are proved in this ...
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Stability and random attractors for a reaction-diffusion equation with multiplicative noiseStability and random attractors for a reaction-diffusion equation with multiplicative noise

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Robinson, James C.; Robinson, James C. (2000-01-01)
We study the asymptotic behaviour of a reaction-diffusion equation, and prove that the addition of multiplicative white ...
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Stochastic Functional Partial Differential Equations: Existence, Uniqueness and Asymptotic Decay PropertyStochastic Functional Partial Differential Equations: Existence, Uniqueness and Asymptotic Decay Property

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Liu, Kai; Liu, Kai (2000-01-01)
Existence and uniqueness of strong solutions for a class of stochastic functional di fferential equations in Hilbert spaces ...
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On Exponential Stability Criteria of Stochastic Partial Differential EquationsOn Exponential Stability Criteria of Stochastic Partial Differential Equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Liu, Kai; Liu, Kai (1999-01-01)
Some criteria for the mean square and almost sure exponential stability of nonlinear stochastic partial differential ...
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Tracking Properties of Trajectories On Random Attracting SetsTracking Properties of Trajectories On Random Attracting Sets

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio (1999-01-01)
The theory of random attracting sets highlights interesting properties of the asymptotic behaviour of some stochastic ...
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Exponential Stability of Mild Solutions of Stochastic Partial Differential Equations with DelaysExponential Stability of Mild Solutions of Stochastic Partial Differential Equations with Delays

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Liu, Kai; Liu, Kai (1999-01-01)
A semilinear stochastic partial differential equation with variable delays is considered. Sufficient conditions for the ...
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Upper Semicontinuity of Attractors for Small Random Perturbations of Dynamical SystemsUpper Semicontinuity of Attractors for Small Random Perturbations of Dynamical Systems

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Robinson, James C.; Robinson, James C. (1998-01-01)
The relationship between random attractors and global attractors for dynamical systems is studied. If a partial differential ...
PhD Thesis
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Atractores y comportamiento finito-dimensional en sistemas dinámicos aleatoriosAtractores y comportamiento finito-dimensional en sistemas dinámicos aleatorios

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio (1998-01-01)
"En el Capítulo 1, presentamos una síntesis de los resultados básicos sobre atractores globales que pueden encontrarse en ...
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On the Pathwise Exponential Stability of Nonlinear Stochastic Partial-Differential EquationsOn the Pathwise Exponential Stability of Nonlinear Stochastic Partial-Differential Equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José (1994-01-01)
Sufficient conditions to get exponential stability for the sample paths (with probability one) of a non-linear monotone ...
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Partial Differential Equations with Delayed Random Perturbations: Existence, Uniqueness and Stability of SolutionsPartial Differential Equations with Delayed Random Perturbations: Existence, Uniqueness and Stability of Solutions

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José (1993-01-01)
We consider a stochastic non–linear Partial Differential Equation with delay which may be regarded as a perturbed equation. ...
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Non-Linear Stochastic Partial Differential Equations with Delays: Existence and Uniqueness of SolutionsNon-Linear Stochastic Partial Differential Equations with Delays: Existence and Uniqueness of Solutions

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (1991-01-01)
The main aim of this paper is to study stochastic PDE's with delay terms. In fact, we prove existence and uniqueness of ...
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Existence and Uniqueness of Solutions for Non-Linear Stochastic Partial Differential EquationsExistence and Uniqueness of Solutions for Non-Linear Stochastic Partial Differential Equations

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (1991-01-01)
We state some results on existence and uniqueness for the solution of non linear stochastic PDEs with deviating arguments. ...
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Asymptotic Exponential Stability of Stochastic Partial Differential Equations with DelayAsymptotic Exponential Stability of Stochastic Partial Differential Equations with Delay

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (1990-01-01)
Sufficient conditions for pathwise asymptotic exponential stability of the solution of the stochastic PDE with delay d x ...
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Ecuaciones en derivadas parciales con perturbaciones estocásticasEcuaciones en derivadas parciales con perturbaciones estocásticas

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Universidad de Extremadura, 1989-01-01)
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Condiciones suficientes de estabilidad para Ecuaciones en Derivadas Parciales estocásticas con retardosCondiciones suficientes de estabilidad para Ecuaciones en Derivadas Parciales estocásticas con retardos

Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (1988-01-01)
Sufficient conditions for pathwise exponential stability of the zero solution of stochastic PDE with deviating argument ...
PhD Thesis
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Algunos resultados de estabilidad de ecuaciones en derivadas parciales estocásticas con retardosAlgunos resultados de estabilidad de ecuaciones en derivadas parciales estocásticas con retardos

Real Anguas, José; Real Anguas, José; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (1988-01-01)
"En esta memoria presentamos una contribución al estudio de la estabilidad en la Ecuaciones en Derivadas Parciales ...