NameCaraballo Garrido, Tomás
DepartmentEcuaciones Diferenciales y Análisis Numérico
Knowledge areaAnálisis Matemático
Professional categoryCatedrático de Universidad
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Dynamics and stability analysis for stochastic 3D Lagrangian-averaged Navier-Stokes equations with infinite delay on unbounded domains

Yang, Shuang; Caraballo Garrido, Tomás; Li, Yangrong (Springer, 2023)
This paper is devoted to investigating mean dynamics and stability analysis for stochastic 3D Lagrangian-averaged Navier–Stokes ...
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The existence and asymptotic behavior of solutions to 3D viscous primitive equations with Caputo fractional time derivatives

Wang, Yejuan; Liu, Yaping; Caraballo Garrido, Tomás (American Institute of Physics, 2023)
On the one hand, the primitive three-dimensional viscous equations for large-scale ocean and atmosphere dynamics are ...
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Stochastic 3D Globally Modified Navier-Stokes Equations: Weak Attractors, Invariant Measures and Large Deviations

Caraballo Garrido, Tomás; Chen, Zhang; Yang, Dandan (Springer, 2023)
This paper is mainly concerned with the asymptotic dynamics of nonautonomous stochastic 3D globally modified Navier-Stokes ...
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Dynamics of multi-valued retarded p-Laplace equations driven by nonlinear colored noise

Wang, Fengling; Caraballo Garrido, Tomás; Li, Yangrong (American Institute of Physics, 2023)
This paper mainly considers the long-term behavior of p-Laplace equations with infinite delays driven by nonlinear colored ...
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The asymptotic behaviour of solutions for stochastic evolution equations with pantograph delay

Liu, Yarong; Wang, Yejuan; Caraballo Garrido, Tomás (World scientific, 2023)
The polynomial stability problem of stochastic delay differential equations has been studied in recent years. In contrast, ...
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Lyapunov functionals and practical stability for stochastic differential delay equations with general decay rate

Caraballo Garrido, Tomás; Ezzine, Faten; Hammami, Mohamed Ali (Bolyai Institute, University of Szeged, 2022)
This paper stands for the almost sure practical stability of nonlinear stochastic differential delay equations (SDDEs) ...
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Asymptotic behavior of a semilinear problem in heat conduction with long time memory and non-local diffusion

Xu, Jiaohui; Caraballo Garrido, Tomás; Valero, José (Elsevier, 2022)
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 mixed nonlinear time-fractional Rayleigh-Stokes equation

Au, Vo Van; Caraballo Garrido, Tomás (AIMS, 2022)
. This paper investigates a nonlinear time-fractional Rayleigh-Stokes equation with mixed nonlinearities containing a ...
Master's Final Project
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Dinámica de un Quimiostato no autónomo con retardo

López de la Cruz, Javier; Caraballo Garrido, Tomás (2022)
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Invariant sample measures and random Liouville type theorem for the two-dimensional stochastic Navier-Stokes equations

Zhao, Caidi; Wang, Jintao; Caraballo Garrido, Tomás (Elsevier, 2022)
In this article, we first prove some sufficient conditions guaranteeing the existence of invariant sample measures for ...
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On a terminal value problem for parabolic reaction–diffusion systems with nonlocal coupled diffusivity terms

NGuyen, Huy Tuan; Caraballo Garrido, Tomás; Khanh Van, Phan Thi; Van Au, Vo (Elsevier, 2022)
In this article, we are interested in investigating the nonlocal nonlinear reaction– diffusion system with final conditions. ...
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Bounded random fluctuations on the input flow in chemostat models with wall growth and non-monotonic kinetics

Caraballo Garrido, Tomás; López de la Cruz, Javier (AIMS Press, 2021)
This paper investigates a chemostat model with wall growth and Haldane consumption kinetics. In addition, bounded random ...
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On initial value and terminal value problems for subdiffusive stochastic Rayleigh-Stokes equation

Caraballo Garrido, Tomás; Ngoc, Tran Bao; Thach, Tran Ngoc; Tuan, Nguyen Huy (AIMS, 2020)
In this paper, we study two stochastic problems for time-fractional RayleighStokes equation including the initial value ...
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Analysis of a stochastic distributed delay epidemic model with relapse and Gamma distribution kernel

Caraballo Garrido, Tomás; El Fatini, Mohamed; El Khalifi, Mohamed; Gerlach, Richard; Pettersson, Roger (Elsevier, 2020)
In this work, we investigate a stochastic epidemic model with relapse and distributed delay. First, we prove that our model ...
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Mathematical methods for the randomized non-autonomous Bertalanffy model

Calatayud Gregori, Julia; Caraballo Garrido, Tomás; Cortés López, Juan Carlos; Jornet Sanz, Marc (Texas State University, 2020)
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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Strong trajectory statistical solutions and Liouville type equation for dissipative Euler equations

Zhao, Caidi; Song, Zhongchun; Caraballo Garrido, Tomás (Elsevier, 2020)
The main aim of this letter is to use the strong compact strong trajectory attractor to construct the strong trajectory ...
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Mild Solutions to Time Fractional Stochastic 2D-Stokes Equations with Bounded and Unbounded Delay

Xu, Jiaohui; Zhang, Zhengce; Caraballo Garrido, Tomás (Springer, 2019)
In this paper, the well-posedness of stochastic time fractional 2D-Stokes equations of order α ∈ (0, 1) containig finite ...
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A stochastic SIRI epidemic model with relapse and media coverage

Caraballo Garrido, Tomás; El Fatini, Mohamed; Pettersson, Roger; Taki, Regragui (American Institute of Mathematical Sciences, 2018)
This work is devoted to investigate the existence and uniqueness of a global positive solution for a stochastic epidemic ...
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Equi-attraction and continuity of attractors for skew-product semiflows

Caraballo Garrido, Tomás; Carvalho, Alexandre Nolasco; Barbosa da Costa, Henrique; Langa Rosado, José Antonio (American Institute of Mathematical Sciences, 2016)
In this paper we prove the equivalence between equi-attraction and continuity of attractors for skew-product semi-flows, ...
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Impulsive stochastic functional differential inclusions driven by a fractional Brownian motion with infinite delay

Boudaoui, Ahmed; Caraballo Garrido, Tomás; Ouahab, Abdelghani (Wiley, 2016)
In this paper, we prove the existence of mild solutions for the following first-order impulsive semilinear stochastic ...
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Applied nonautonomous and random dynamical systems

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

Caraballo Garrido, Tomás; Xiaoying, Han; Schmalfuss, Björn; Valero Cuadra, José (2016)
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 delay

Boudaoui, Ahmed; Caraballo Garrido, Tomás; Ouahab, Abdelghani (Taylor & Francis, 2016)
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.
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Existence and stability results for semilinear systems of impulsive stochastic differential equations with fractional Brownian motion

Blouhi, Tayeb; Caraballo Garrido, Tomás; Ouahab, Abdelghani (Taylor & Francis, 2016)
Some results on the existence and uniqueness of mild solution for a system of semilinear impulsive differential equations ...
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New trends on nonlinear dynamics and its applications

Caraballo Garrido, Tomás; García Guirao, Juan Luis (American Institute of Mathematical Sciences, 2015)
This paper is the Preface of a special issue devoted to Nonlinear Dynamics and Complexity generated by the contributions ...
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Effects of additive and multiplicative noise on the dynamics of a parabolic equation

Caraballo Garrido, Tomás; Colucci, Renato (Natural Sciences Publishing Corporation, 2015)
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 delays

Caraballo Garrido, Tomás; Xiaoying, Han; Kloeden, Peter E. (Society for Industrial and Applied Mathematics, 2015)
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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Random attractors for stochastic lattice systems with non-Lipschitz non-linearity

Caraballo Garrido, Tomás; Morillas Jurado, Francisco; Valero Cuadra, José (2012)
In this paper we study the asymptotic behaviour of solutions of a first-order stochastic lattice dynamical system with an ...
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Stability of Gradient Semigroups Under Perturbations

Aragão Costa, Eder Ritis; Caraballo Garrido, Tomás; Carvalho, Alexandre Nolasco; Langa Rosado, José Antonio (2011)
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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Three-dimensional system of globally modified Navier-Stokes equations with delay

Caraballo Garrido, Tomás; Real Anguas, José; Márquez, Antonio M. (2010)
We prove the existence and uniqueness of strong solutions of a three-dimensional system of globally modified Navier–Stokes ...
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A gradient-like non autonomous evolution process

Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Rivero Garvía, Luis Felipe; Carvalho, Alexandre Nolasco (2009)
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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Synchronization of Systems with Multiplicative Noise

Caraballo Garrido, Tomás; Kloeden, Peter E.; Neuenkirch, Andreas (2008)
The synchronization of Stratonovich stochastic di erential equations (SDE) with a one-sided dissipative Lipschitz drift ...
Presentation
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Sobre la existencia de atractores para ecuaciones aleatorias de reacción-difusión con retardos

Caraballo Garrido, Tomás; Garrido Atienza, María José; Schmalfuss, Björn; Valero Cuadra, José (2007)
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 delay

Caraballo Garrido, Tomás; Kloeden, Peter E.; Marín Rubio, Pedro (2007)
The upper semi-continuous convergence of approximate attractors for an infinite delay differential equation of logistic ...
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Pullback and forward attractors for a 3D Lans-alpha model with delay

Caraballo Garrido, Tomás; Márquez Durán, Antonio Miguel; Real Anguas, José (2006)
We analyse the asymptotic behaviour of a 3D Lagrangian averaged Navier-Stokes -model (3D LANS) with delays. In fact, we ...
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The effect of noise on the chafee-infante equation: a nonlinear case study

Caraballo Garrido, Tomás; Crauel, Hans; Langa Rosado, José Antonio; Robinson, James C. (2006)
We investigate the effect of perturbing the Chafee-Infante scalar reaction diffusion equation, ut−Δu = βu−u3, by noise. ...
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Global and Pullback Attractors of Set-Valued Skew Product Flows

Caraballo Garrido, Tomás; Kloeden, Peter E.; Marín Rubio, Pedro (2006)
We investigate the asymptotic behaviour of a general set-valued skew product flow (SVSPF), that is, a set-valued cocycle ...
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On the stochastic 3D-Lagrangian averaged Navier-Stokes Alpha-Model with finite delay

Caraballo Garrido, Tomás; Márquez Durán, Antonio Miguel; Real Anguas, José (2005)
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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Addendum To "Global Attractors for Multivalued Random Dynamical Systems'' [Nonlinear Analysis 48(2002) 805-829]

Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Valero Cuadra, José (2005)
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 2D-Navier-Stokes Equations with Delays

Caraballo Garrido, Tomás; Real Anguas, José (2003)
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 equations

Caraballo Garrido, Tomás; Garrido Atienza, María José; Real Anguas, José (2003)
Some results on the pathwise asymptotic stability of solutions to stochastic partial differential equations are proved. ...
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On the decay rate of solutions of non-autonomous differential systems

Caraballo Garrido, Tomás (2001)
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 noise

Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Cuadra Valero, José (2001)
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.
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On Exponential Stability Criteria of Stochastic Partial Differential Equations

Caraballo Garrido, Tomás; Liu, Kai (1999)
Some criteria for the mean square and almost sure exponential stability of nonlinear stochastic partial differential ...