Article
Yang, Shuang; Yang, Shuang; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Li, Yangrong; Li, Yangrong (Elsevier, 20230405)
In this paper we investigate stochastic dynamics and invariant measures for stochastic 3D Lagrangianaveraged NavierStokes ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Uzal, José M.; Uzal, José M. (Springer, 20230210)
In this paper we study the asymptotic behaviour of multivalued processes which are under the influence of impulsive action. ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ezzine, Faten; Ezzine, Faten; Hammami, Mohamed Ali; Hammami, Mohamed Ali (Bolyai Institute, University of Szeged, 20221201)
This paper stands for the almost sure practical stability of nonlinear stochastic
differential delay equations (SDDEs) ...

Article
Liu, Yarong; Liu, Yarong; Wang, Yejuan; Wang, Yejuan; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (SIAM, 20221007)
In this paper, we study the full compressible NavierStokes system in a bounded domain Ω⊂R3
, where the viscosity and ...

Article
Wang, Jingyu; Wang, Jingyu; Wang, Yejuan; Wang, Yejuan; Yang, Lin; Yang, Lin; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (AIMS, 20221001)
A nonautonomous stochastic delay wave equation with linear memory and nonlinear
damping driven by additive white noise ...

Article
Xu, Jiaohui; Xu, Jiaohui; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Valero, José; Valero, José (AIMS, 20221001)
In this paper, it is first addressed the wellposedness of weak solutions to a nonlocal partial differential equation with ...

Article
Wang, Jingyu; Wang, Jingyu; Wang, Yejuan; Wang, Yejuan; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (AIMS, 20221001)
This paper is devoted to the asymptotic behavior of solutions to a nonautonomous stochastic wave equation with infinite ...

Article
Yang, Dandan; Yang, Dandan; Chen, Zhang; Chen, Zhang; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Springer, 20220927)
This paper investigates the dynamics of a class of threedimensional
globally modified NavierStokes equations with double ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Mchiri, Lassaad; Mchiri, Lassaad; Mohsen, Belfeki; Mohsen, Belfeki; Rhaima, Mohamed; Rhaima, Mohamed (Wiley, 20220927)
In this article, we investigate the existence and uniqueness of solution of controlled
hybrid neutral stochastic di erential ...

Article
Yang, Shuang; Yang, Shuang; Li, Yangrong; Li, Yangrong; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (AIP Publishing, 20220911)
In this paper, two problems related to FitzHughNagumo lattice systems are analyzed. The first one is
concerned with the ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ezzine, Faten; Ezzine, Faten; Hammami, Mohamed Ali; Hammami, Mohamed Ali (Springer, 20220901)
The Lyapunov approach is one of the most effective and efficient methods for the inves tigation of the stability of ...

Article
Xu, Jiaohui; Xu, Jiaohui; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Valero, José; Valero, José (Elsevier, 20220801)
In this paper, the asymptotic behavior of a semilinear heat equation with long time memory
and nonlocal diffusion is ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Cavaterra, Cecilia; Cavaterra, Cecilia (20220801)
In this paper we consider a model describing the evolution of a nematic liquid crystal flow with delay external forces. ...

Article
Xu, Jiaohui; Xu, Jiaohui; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Texas State University, 20220619)
We analyze the wellposedness of two versions of a stochastic time
delay fractional 2DStokes model with nonlinear ...

Master's Final Project
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; López de la Cruz, Javier; López de la Cruz, Javier (20220615)

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Mchiri, Lassaad; Mchiri, Lassaad; Mohsen, Belfeki; Mohsen, Belfeki (Wiley, 20220301)
In this paper, we study the ηstability in qth moment (η.s.q.m) of hybrid neutral
stochastic differential equations with ...

Article
Mchiri, Lassaad; Mchiri, Lassaad; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Rhaima, Mohamed; Rhaima, Mohamed (Springer, 20220225)
In this paper, we investigate the partial asymptotic stability (PAS) of neutral
pantograph stochastic differential equations ...

Article
; ; Benhadri, Mimia; Benhadri, Mimia; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Scopus, 20220222)
New criteria ensuring global asymptotic stability of the zero solution for a class of linear neutral differential equations ...

Article
Zhao, Caidi; Zhao, Caidi; Wang, Jintao; Wang, Jintao; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Elsevier, 20220217)
In this article, we first prove some sufficient conditions guaranteeing the existence of invariant sample
measures for ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Mchiri, Lassaad; Mchiri, Lassaad; Rhaima, Mohamed; Rhaima, Mohamed (Taylor & Francis, 20220201)
In this paper, by using the Gronwall inequality, we show two new results on the UlamHyers and the UlamHyersRassias stabilities of neutral stochastic functional differential
equations. Two examples illustrating our results are exhibited.

Article
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, 20220124)
In this paper we consider the nonautonomous semilinear parabolic problems with timedependent linear
operators
ut + A(t)u ...

Article
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, 20220110)
In this article, we are interested in investigating the nonlocal nonlinear reaction–
diffusion system with final conditions. ...

Article
Xu, Jiaohui; Xu, Jiaohui; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (SIAM, 20220101)
This paper is devoted to investigating the wellposedness and asymptotic behavior of a class of stochastic
5 nonlocal ...

Article
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, 20220101)
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 ...

Article
Benhadri, Mimia; Benhadri, Mimia; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Springer, 20211111)
In this paper, we investigate the existence of positive periodic solutions
for an nspecies LotkaVolterra system with ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Mchiri, Lassaad; Mchiri, Lassaad; Mohsen, Belfeki; Mohsen, Belfeki; Rhaima, Mohamed; Rhaima, Mohamed (Elsevier, 20211101)
In this paper we focus on the pth moment exponential stability of neutral stochastic pantograph differential equations ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Belfeki, Mohsen; Belfeki, Mohsen; Mchiri, Lassaad; Mchiri, Lassaad; Rhaima, Mohamed; Rhaima, Mohamed (Elsevier, 20211001)
In this paper we investigate the hstability in pth moment of neutral pantograph stochastic differential equations with ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; El Fatini, Mohamed; El Fatini, Mohamed; El Khalifi, Mohamed; El Khalifi, Mohamed; Rathinasamy, Anandaraman; Rathinasamy, Anandaraman (Taylor & Francis, 20210930)
This paper studied a stochastic epidemic model of the spread of the novel coronavirus (COVID19). Severe factors impacting ...

PhD Thesis
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Schiabel, Karina; Schiabel, Karina; Boldrin Belluzi, Maykel; Boldrin Belluzi, Maykel (20210921)
In this work we consider the singularly nonautonomous semilinear parabolic problem
ut + A(t)u = F(u); t > ;
u( ) = u0;
in ...

Article
Liu, Yarong; Liu, Yarong; Wang, Yejuan; Wang, Yejuan; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (World scientific, 20210901)
We consider stochastic 2DStokes equations with unbounded delay in fractional power
spaces and moments of order p ≥ 2 ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; López de la Cruz, Javier; López de la Cruz, Javier; Rapaport, Alain; Rapaport, Alain (World scientific, 20210901)
This paper investigates the dynamics of a model of two chemostats connected by Fickian diffusion with bounded random ...

Article
Benhadri, Mimia; Benhadri, Mimia; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (DOAJ, 20210901)
This paper addresses the stability study for nonlinear neutral differ ential equations. Thanks to a new technique based ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ezzine, Faten; Ezzine, Faten; Hammami, Mohamed Ali; Hammami, Mohamed Ali (Springer, 20210828)
This paper is concerned with the almost sure partial practical stability of stochastic differential equations
with general ...

Article
Xu, Jiaohui; Xu, Jiaohui; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Springer, 20210817)
This paper is concerned with the asymptotic behavior of solutions to nonlocal stochastic partial differential equations ...

Article
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, 20210804)
ct. In this paper we consider the singularly nonautonomous evolution
problem
ut + A(t)u = f(t), τ < t < τ + T; u(τ) = u0 ...

Article
Tuan Nguyen, Anh; Tuan Nguyen, Anh; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Tuan, Nguyen Huy; Tuan, Nguyen Huy (Elsevier, 20210801)
In this work, we investigate the IVP for a timefractional fourthorder equation with nonlinear
source terms. More ...

Article
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, 20210801)
In this paper, a nonlinear timefractional Volterra equation with nonsingular MittagLeffler kernel in Hilbert spaces is ...

Article
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, 20210715)
This paper is concerned with the mathematical analysis of terminal value problems for a
stochastic nonclassical diffusion ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ezzine, Faten; Ezzine, Faten; Hammami, Mohamed Ali; Hammami, Mohamed Ali (Springer, 20210624)
In this paper, we investigate the problem
of stability of timevarying stochastic perturbed singular systems by using ...

Article
NGuyen, Huy Tuan; NGuyen, Huy Tuan; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Tran, Ngoc Thach; Tran, Ngoc Thach (IOS Press, 20210609)
In this paper, we study two terminal value problems (TVPs) for stochastic biparabolic equations perturbed by standard ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Mchiri, Lassaad; Mchiri, Lassaad; Rhaima, Mohamed; Rhaima, Mohamed (Springer, 20210603)
In this paper, we investigate the partial practical exponential stability of neutral stochastic functional differential ...

Article
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], 20210501)
In this corrigendum we correct an error in our paper [T. Caraballo, R. Colucci, J. LópezdelaCruz and A. Rapaport. A way ...

Article
Zhao, Caidi; Zhao, Caidi; Jiang, Huite; Jiang, Huite; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Elsevier, 20210405)
We first verify the global wellposedness of the impulsive reactiondiffusion equations on infinite lattices. Then we ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Boudaoui, Ahmed; Boudaoui, Ahmed; Blouhi, Tayeb; Blouhi, Tayeb (Taylor and Francis Online, 20210217)
We prove an existence and uniqueness result of mild solution for a system of stochastic semilinear differential equations ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ezzine, Faten; Ezzine, Faten; Hammami, Mohamed Ali; Hammami, Mohamed Ali (Springer, 20210209)
The approach of Lyapunov functions is one of the most efficient ones for the investigation of the stability of stochastic ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; López de la Cruz, Javier; López de la Cruz, Javier (AIMS Press, 20210204)
This paper investigates a chemostat model with wall growth and Haldane consumption kinetics. In addition, bounded random ...

Article
Zhao, Caidi; Zhao, Caidi; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Lukaszewicz, Grzegorz; Lukaszewicz, Grzegorz (Elsevier [Commercial Publisher], Academic Press [Associate Organisation], 20210128)
In this article, the authors investigate the system of Schr odinger and KleinGordon equations with Yukawa coupling. They ...

Article
Wang, Yejuan; Wang, Yejuan; Liu, Yarong; Liu, Yarong; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Springer, 20210102)
In this paper, we investigate stochastic evolution equations with unbounded delay in fractional power spaces perturbed by ...

Article
Wang, Yejuan; Wang, Yejuan; Liu, Yarong; Liu, Yarong; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Springer, 20210102)
In this paper, we investigate stochastic evolution equations with unbounded delay in fractional power spaces perturbed by ...

Article
Yang, Lin; Yang, Lin; Wang, Yejuan; Wang, Yejuan; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (AIMS, 20210101)
In this paper we investigate the regularity of global attractors and
of exponential attractors for two dimensional ...

Article
Netchaoui, Sana; Netchaoui, Sana; Hammami, Mohamed Ali; Hammami, Mohamed Ali; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (American Institute of Mathematical Sciences, 20210101)
We show the existence of an exponential attractor for nonautonomous dynamical system with bounded delay. We considered ...

Article
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, 20210101)
In this work, we study permanence of hyperbolicity for autonomous differential equations under nonautonomous random/stochastic ...

Article
Shaikhet, Leonid; Shaikhet, Leonid; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Taylor & Francis, 20201208)
Stability of nonlinear delay evolution equation with stochastic perturbations is considered. It is shown that if the level ...

Article
López de la Cruz, Javier; López de la Cruz, Javier; PérezAranda Redondo, María; PérezAranda 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, 20201201)
This work discloses an epidemiological mathematical model to predict an empirical treatment for dogs infected by Pseudomonas ...

Article
Wang, Jintao; Wang, Jintao; Zhao, Caidi; Zhao, Caidi; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Elsevier, 20201201)
This article investigates the threedimensional globally modified NavierStokes equations with unbounded variable delays. ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Guo, Boling; Guo, Boling; Tuan, Nguyen Huy; Tuan, Nguyen Huy; Wang, Renhai; Wang, Renhai (Cambrigde Core, 20201105)
This paper is concerned with the asymptotic behavior of solutions to a class of nonautonomous stochastic nonlinear wave ...

Article
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, 20201029)
We revisit the chemostat model with Haldane growth function, here subject to bounded random disturbances on the input flow ...

Article
Boukanjime, Brahim; Boukanjime, Brahim; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; El Fatini, Mohamed; El Fatini, Mohamed; El Khalifi, Mohamed; El Khalifi, Mohamed (Elsevier, 20201016)
In this paper, we analyze a stochastic coronavirus (COVID19) epidemic model which is perturbed by both white noise and ...

Article
Xu, Jiaohui; Xu, Jiaohui; Zhang, Zhengce; Zhang, Zhengce; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Elsevier [Commercial Publisher], Academic Press [Associate Organisation], 20200915)
The paper addresses a kind of nonautonomous nonlocal parabolic equations when the external force contains hereditary ...

Article
Liang, Tongtong; Liang, Tongtong; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Wang, Yejuan; Wang, Yejuan (Springer, 20200818)
In this paper, fractionally dissipative 2D quasigeostrophic equations with an external force containing infinite delay ...

Article
Wang, Yejuan; Wang, Yejuan; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (American Institute of Mathematical Sciences (AIMS), 20200801)
In this paper, we first prove that the property of being a gradientlike general dynamical system and the existence of a ...

Article
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, 20200630)
In this paper, we study two stochastic problems for timefractional RayleighStokes equation including the initial value ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Márquez Durán, Antonio Miguel; Márquez Durán, Antonio Miguel (AIMS PressAIMS Press, 20200624)
In this paper we consider a nonautonomous NavierStokesVoigt model including a variety of delay terms in a unified ...

Article
NGuyen, Huy Tuan; NGuyen, Huy Tuan; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (American Mathematical Society, 20200611)
In this paper, we consider fractional nonclassical diffusion equations under two forms: initial value problem and terminal ...

Article
Rodrígues, H. M.; Rodrígues, H. M.; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Nakassima, G. K.; Nakassima, G. K. (Springer, 20200605)
In this paper we study the robustness of the exponential dichotomy
in nonautonomous linear ordinary differential equations ...

Article
Zhao, Caidi; Zhao, Caidi; Li, Yanjiao; Li, Yanjiao; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Elsevier, 20200601)
In this article, we first prove, from the viewpoint of infinite dynamical system, sufficient conditions ensuring the ...

Article
Sun, Wenlong; Sun, Wenlong; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Han, Xiaoying; Han, Xiaoying; Kloeden, Peter E.; Kloeden, Peter E. (Elsevier, 20200601)
A nonautonomous free boundary model for tumor growth is studied. The model consists of a nonlinear reaction diffusion ...

PhD Thesis
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Xu, Jiaohui; Xu, Jiaohui (20200520)
On the one hand, the classical heat equation∂tu= ∆udescribes heatpropagation in a homogeneous medium, while the time ...

Article
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, 20200501)
In this paper, we study a stochastic epidemic model with isolation and nonlinear incidence. In particular, we propose a ...

PhD Thesis
Langa Rosado, José Antonio; Langa Rosado, José Antonio; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Galadí García, Javier Alejandro; Galadí García, Javier Alejandro (20200421)
This thesis applies the great advances of modern dynamical systems theory
(DST) to consciousness. Consciousness, or ...

Article
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, 20200401)
In this work, we investigate a stochastic epidemic model with relapse and distributed delay. First, we prove that our model ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Pereira da Silva, Alex; Pereira da Silva, Alex (Mathematica Scandinavica [Independent Journal], 20200329)
This paper is devoted to analyze the stability of the economy according to an extended version of Kaldor's economic growth ...

Article
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), 20200201)
The existence and uniqueness of mild solution of an impulsive stochastic system driven by a Rosenblatt process is analyzed ...

Article
Zhao, Caidi; Zhao, Caidi; Song, Zhongchun; Song, Zhongchun; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Elsevier, 20200101)
The main aim of this letter is to use the strong compact strong trajectory attractor to construct the strong trajectory ...

Article
Benhadri, Mimia; Benhadri, Mimia; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Zeghdoudi, Halim; Zeghdoudi, Halim (Taylor and Francis, 20200101)
In this paper we prove some results on the mean square asymptotic stability of a class of neutral stochastic differential ...

Article
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, 20200101)
In this article we analyze the randomized nonautonomous Bertalanffy model x 0 (t, ω) = a(t, ω)x(t, ω) + b(t, ω)x(t, ω)
2/3, ...

Article
Benhadri, Mimia; Benhadri, Mimia; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Zeghdoudi, Halim; Zeghdoudi, Halim (AGH University of Science and Technology Press, 20200101)
We investigate the existence of positive periodic solutions of a nonlinear LotkaVolterra competition system with deviating ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Valero Cuadra, José; Valero Cuadra, José (Springer, 20200101)
In this paper we establish a strong comparison principle for a nonautonomous differential inclusion with a forcing term ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Teamah, Abd ElMoneim Anwar; Teamah, Abd ElMoneim Anwar; ElBagoury, Abd AlAziz Hosni; ElBagoury, Abd AlAziz Hosni (Taylor and Francis, 20200101)
This paper considers a new model in search theory to find a randomly located target in the 3dimensional space. An ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ezzine, Faten; Ezzine, Faten; Hammami, Mohamed Ali; Hammami, Mohamed Ali; Mchiri, Lassaad; Mchiri, Lassaad (Taylor & Francis, 20200101)
In this paper, practical stability with respect to a part of the variables of nonlinear stochastic differential equations ...

Article
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, 20191205)
In this work we present results to ensure a weak upper semicontinuity for a family of impulsive cocycle attractors of ...

Article
Liu, Linfang; Liu, Linfang; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Springer, 20191201)
Some results concerning a stochastic 2D NavierStokes system when the external forces contain hereditary characteristics ...

Article
Xu, Jiaohui; Xu, Jiaohui; Zhang, Zhengce; Zhang, Zhengce; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Springer, 20191119)
In this paper, the wellposedness of stochastic time fractional 2DStokes equations of order α ∈ (0, 1) containig finite ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Tuan, Nguyen Huy; Tuan, Nguyen Huy; Ngoc, Tran Bao; Ngoc, Tran Bao; Zhou, Yong; Zhou, Yong (IOP Science, 20191115)
We consider the terminal value problem (or called nal value problem, initial inverse prob
lem, backward in time problem) ...

Article
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, 20191001)
In this paper, we analyze the use of the OrnsteinUhlenbeck process to model dynamical systems subjected to bounded noisy ...

Article
Zhang, Tian; Zhang, Tian; Chen, Huabin; Chen, Huabin; Yuan, Chenggui; Yuan, Chenggui; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (American Institute of Mathematical Sciences, 20191001)
In this paper, under a local Lipschitz condition and a monotonicity condition, the problems on the existence and uniqueness ...

PhD Thesis
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Pereira da Silva, Alex; Pereira da Silva, Alex (20190906)
The longrun aim of this thesis is to solve delay differential equations with infinite delay of the type d dt u(t) = ...

Article
Boudaoui, Ahmed; Boudaoui, Ahmed; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Blouhi, Tayeb; Blouhi, Tayeb (De Gruyter, 20190901)
In this paper, we prove some existence, uniqueness and HyersUlam stability results for the coupled random fixed point of ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Cortés López, Juan Carlos; Cortés López, Juan Carlos; Navarro Quilés, Ana; Navarro Quilés, Ana (Elsevier, 20190901)
We randomize the following class of linear differential equations with delay, x 0 τ (t) = axτ(t) + bxτ(t − τ), t > 0, and ...

Article
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, 20190801)
In this work the theory of generalized processes is used to describe the dynamics of a nonautonomous multivalued problem ...

Article
Xu, Jiaohui; Xu, Jiaohui; Zhang, Zhengce; Zhang, Zhengce; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Elsevier, 20190801)
This paper is concerned with the wellposedness and dynamics of delay impulsive fractional stochastic evolution equations ...

Article
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, 20190801)
In this paper we study a new way to model noisy input flows in the chemostat model, based on the OrnsteinUhlenbeck process. ...

Article
Liu, Linfang; Liu, Linfang; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E. (De Gruyter, 20190601)
The existence and uniqueness of global solutions for a fractional functional differential equation is established. The ...

Article
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, 20190601)
Focusing on epidemic model in random environments, this paper uses white noise and Lévy noise to model the dynamics of the ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato; Guerrini, Luca; Guerrini, Luca (American Institute of Mathematical, 20190601)
In this article we consider a model introduced by Ucar in order to simply describe chaotic behaviour with a one dimensional ...

Article
Xu, Jiaohui; Xu, Jiaohui; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (American Institute of Mathematical Sciences, 20190601)
This paper is first devoted to the local and global existence of mild solutions for a class of fractional impulsive ...

Article
Zhao, Caidi; Zhao, Caidi; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Elsevier, 20190515)
We first prove the existence and regularity of the trajectory attractor for a threedimensional system of globally modified ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato; Guerrini, Luca; Guerrini, Luca (American Institute of Mathematical Sciences, 20190301)
In this paper, we consider the environmental defensive expenditures model with delay proposed by Russu in P. Russu, Hopf ...

Article
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, 20190201)
This paper focuses on a pumpedstorage generating system with a reversible Francis turbine and presents an innovative ...

Article
Blouhi, Tayeb; Blouhi, Tayeb; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ouahab, Abdelghani; Ouahab, Abdelghani (Casa Cărţii de Ştiinţă ClujNapoca, 20190201)
In this paper we prove the existence of mild solutions for a firstorder impulsive semilinear stochastic differential ...

Article
Benhadri, Mimia; Benhadri, Mimia; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Zeghdoudi, Halim; Zeghdoudi, Halim (Taylor & Franci, 20190101)
In this paper we prove some results on the existence of solutions and
the mean square asymptotic stability for a class of ...

Article
Liu, Linfang; Liu, Linfang; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Marín Rubio, Pedro; Marín Rubio, Pedro (Elsevier, 20181205)
Some results related to 2D NavierStokes equations when the external force contains hereditary characteristics involving ...

Article
Liu, Linfang; Liu, Linfang; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Fu, Xianlong; Fu, Xianlong (American Institute of Mathematical Sciences, 20181201)
The existence and uniqueness of stationary solutions to an incompressible nonNewtonian fluid are first established. The ...

Article
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, 20181105)
In this paper we obtain a detailed description of the global and cocycle attractors for the skewproduct semiflows induced ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Herrera Cobos, Marta; Herrera Cobos, Marta; Marín Rubio, Pedro; Marín Rubio, Pedro (Cambridge University Press, 20181001)
In this paper, the existence and uniqueness of weak and strong solutions for a
nonautonomous nonlocal reactiondiffusion ...

PhD Thesis
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; López de la Cruz, Javier; López de la Cruz, Javier (20180628)

PhD Thesis
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Liu, Linfang; Liu, Linfang (20180628)
Based on the theory of functional diferential equations, theory of semigroup, theory of random dynamical systems and theory ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Herrera Cobos, Marta; Herrera Cobos, Marta; Marín Rubio, Pedro; Marín Rubio, Pedro (American Institute of Mathematical Sciences, 20180501)
In this paper, the existence of regular pullback attractors as well as their upper semicontinuous behaviour in H1norm are ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Herrera Cobos, Marta; Herrera Cobos, Marta; Marín Rubio, Pedro; Marín Rubio, Pedro (Elsevier, 20180301)
In this paper, we focus on studying the existence of attractors in the phase spaces L2(Ω) and Lp(Ω) (among others) for ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Keraani, Sami; Keraani, Sami (Taylor & Francis, 20180101)
In this article, a stochastic version of a SIR nonautonomous model previously introduced in Kloeden and Kozyakin (2011) ...

Article
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, 20180101)
This work is devoted to investigate the existence and uniqueness of a global positive solution for a stochastic epidemic ...

Article
Berrhazi, Badreddine; Berrhazi, Badreddine; El Fatini, Mohamed; El Fatini, Mohamed; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Pettersson, Roger; Pettersson, Roger (American Institute of Mathematical Sciences, 20180101)
Some diseases such as herpes, bovine and human tuberculosis exhibit
relapse in which the recovered individuals do not ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato; Guerrini, Luca; Guerrini, Luca (American Institute of Mathematical Sciences, 20180101)
A predator prey model with nonlinear harvesting (Holling typeII) with both constant and distributed delay is considered. ...

Final Degree Project
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Lindes Colón, Mercedes; Lindes Colón, Mercedes (20180101)
Mathematical modeling, currently, is a very important element in health system, since it allows studying the incidence, ...

Presentation
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 (20180101)
In this talk, some random and stochastic disturbances in the chemostat model will be analyzed by making use of the modern ...

Article
Xu, Beibei; Xu, Beibei; Chen, Diyi; Chen, Diyi; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Springer, 20180101)
The research proposed in this paper focuses on the dynamic evolution of a
hydraulicmechanicalelectric system under the ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato; Guerrini, Luca; Guerrini, Luca (Wiley, 20180101)
We study a continuous Hénon system obtained by considering the discrete original model in continuous time. While the ...

Article
Samprogna, Rodrigo Antonio; Samprogna, Rodrigo Antonio; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (American Institute of Mathematical Sciences, 20180101)
In this work we prove the existence of solution for a pLaplacian nonautonomous problem with dynamic boundary and infinite ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Sonner, Stefanie; Sonner, Stefanie (American Institute of Mathematical Sciences, 20171201)
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.

Article
Munhoz Rodrigues, Hildebrando; Munhoz Rodrigues, Hildebrando; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Fuzeto Gameiro, Marcio; Fuzeto Gameiro, Marcio (American Institute of Mathematical Sciences, 20171101)
The objective of this paper is to study a perturbed linear hyperbolic
differential equation. The first part of this work ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Hammami, Mohamed Ali; Hammami, Mohamed Ali; Mchiri, Lassaad; Mchiri, Lassaad (Elsevier, 20171101)
This paper is devoted to the investigation of the practical exponential stability of impulsive stochastic functional ...

Article
Liu, Linfang; Liu, Linfang; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Elsevier, 20170915)
In this paper we investigate the wellposedness and dynamics of a fractional stochastic integrodifferential equation ...

Article
Boudaoui, Ahmed; Boudaoui, Ahmed; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (American Institute of Mathematical Sciences, 20170901)
This paper is concerned with the existence and continuous dependence
of mild solutions to stochastic differential equations ...

Article
Liu, Linfang; Liu, Linfang; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E. (Springer, 20170901)
The existence and limiting behavior of the solutions of stochastic parabolic problems with thermal memory are investigate ...

Article
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, 20170801)
In this paper we study two stochastic chemostat models, with and without wall growth, driven by a white noise. Specifically, ...

Article
Blouhi, Tayeb; Blouhi, Tayeb; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ouahab, Abdelghani; Ouahab, Abdelghani (Taylor & Francis, 20170801)
In this paper we correct an error made in our paper [Blouhi, T.; Caraballo,
T.; Ouahab, A. Existence and stability results ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Herrera Cobos, Marta; Herrera Cobos, Marta; Marín Rubio, Pedro; Marín Rubio, Pedro (American Institute of Mathematical Sciences, 20170701)
In this paper, the existence of solution for a pLaplacian parabolic equation with nonlocal diffusion is established. To ...

Article
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, 20170701)
We show existence and uniqueness of solutions for a nonclassical and nonautonomous diffusion equation with infinite delay ...

Article
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, 20170701)
The longtime behavior of solutions (more precisely, the existence of random pullback attractors) for an integrodifferential ...

Final Degree Project
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Ruiz González, Ángeles; Ruiz González, Ángeles (20170601)
In this work we will study the theory of dynamical systems with application to a chemostat. Starting with the autonomous ...

Final Degree Project
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Minuesa Abril, María José; Minuesa Abril, María José (20170601)
Nowadays, mathematical models are one of the most popular tools to study
epidemics due to the fact that they enable to ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato (Springer, 20170401)
We provide a qualitative description of microstructure formation and coarsening phenomena for the solutions of a singularly ...

Article
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, 20170315)
In this work, we deal with several different notions of attractors that may appear in the impulsive nonautonomous case ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato (Wiley, 20170201)
In this paper we analyze a model presenting formation of microstructure depending on the parameters and the initial data. ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato (American Institute of Mathematical Sciences, 20170101)
In this article, a random and a stochastic version of a SIR nonautonomous model previously introduced in P. E. Kloeden and ...

Article
Liu, Linfang; Liu, Linfang; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Fu, Xianlong; Fu, Xianlong (International Press, 20170101)
We first study the wellposedness of a nonautonomous incompressible nonNewtonian fluid with delay. The existence of ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Obaya García, Rafael; Obaya García, Rafael (IOP Publishing, 20170101)
The global attractor of a skew product semiflow for a nonautonomous
differential equation describes the asymptotic behaviour ...

Presentation
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 (20170101)
In this talk, some different ways of modeling stochastic chemostats will be presented in order to obtain much more realistic ...

Article
Diop, Mamadou Abdoul; Diop, Mamadou Abdoul; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Zene, Mahamat Mahamat; Zene, Mahamat Mahamat (World Scientific Publishing, 20161201)
In this work we study the existence, uniqueness and asymptotic behavior of mild solutions for neutral stochastic partial ...

Article
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, 20161101)
In this paper we prove the equivalence between equiattraction and continuity of attractors for skewproduct semiflows, ...

Article
Diop, Mamadou Abdoul; Diop, Mamadou Abdoul; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Mané, Aziz; Mané, Aziz (Wiley, 20161001)
In this work we study the existence and uniqueness of mild solutions for stochastic partial integrodifferential equations ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato; Han, Xiaoying; Han, Xiaoying (Elsevier, 20161001)
In this paper we study a semiKolmogorov type of population model, arising
from a predatorprey system with indirect ...

Article
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, 20161001)
This work is devoted to the construction of impulsive sets in Rn. In the literature, there are many examples of impulsive ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato (American Institute of Mathematical Sciences, 20160901)
In this work we study semiKolmogorov models for predation with both the carrying capacities and the indirect effects ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio (American Institute of Mathematical Sciences, 20160801)
The structure of attractors for differential equations is one of the main topics
in the qualitative theory of dynamical ...

PhD Thesis
Marín Rubio, Pedro; Marín Rubio, Pedro; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Herrera Cobos, Marta; Herrera Cobos, Marta (20160623)
En las últimas décadas muchos investigadores han estado interesados en estudiar problemas no locales por su utilidad en ...

Article
Boudaoui, Ahmed; Boudaoui, Ahmed; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ouahab, Abdelghani; Ouahab, Abdelghani (Wiley, 20160401)
In this paper, we prove the existence of mild solutions for the following firstorder impulsive semilinear stochastic ...

Article
Blouhi, Tayeb; Blouhi, Tayeb; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ouahab, Abdelghani; Ouahab, Abdelghani (Taylor & Francis, 20160101)
Some results on the existence and uniqueness of mild solution for a system
of semilinear impulsive differential equations ...

Book
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Han, Xiaoying; Han, Xiaoying (Springer, 20160101)

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Xiaoying, Han; Xiaoying, Han; Schmalfuss, Björn; Schmalfuss, Björn; Valero Cuadra, José; Valero Cuadra, José (20160101)
In this paper we investigate the long term behavior of a stochastic lattice dynamical system with a diffusive nearest ...

Article
Boudaoui, Ahmed; Boudaoui, Ahmed; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ouahab, Abdelghani; Ouahab, Abdelghani (Taylor & Francis, 20160101)
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
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, 20160101)
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
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, 20160101)
In this paper we study a simple chemostat model influenced by white
noise which makes this kind of models more realistic. ...

Presentation
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), 20160101)
In this survey we provide an introduction to the theory of impulsive dynamical systems in both the autonomous and nonautonomous ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; García Guirao, Juan Luis; García Guirao, Juan Luis (American Institute of Mathematical Sciences, 20151201)
This paper is the Preface of a special issue devoted to Nonlinear Dynamics and Complexity generated by the contributions ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato; Xiaoying, Han; Xiaoying, Han (Springer, 20150630)
We investigate the long term dynamics for a predation model of
Plankton community with indirect effects, under fluctuating ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Herrera Cobos, Marta; Herrera Cobos, Marta; Marín Rubio, Pedro; Marín Rubio, Pedro (Springer, 20150617)
In this paper, we consider a nonautonomous nonlocal reactiondiffusion
equation with a small perturbation in the nonlocal ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Hammami, Mohamed Ali; Hammami, Mohamed Ali; Mchiri, Lassaad; Mchiri, Lassaad (Taylor & Francis, 20150604)
The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Hammami, Mohamed Ali; Hammami, Mohamed Ali; Mchiri, Lassaad; Mchiri, Lassaad (Springer, 20150423)
In this paper we investigate the almost sure practical stability for a class of stochastic functional evolution equations. ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Xiaoying, Han; Xiaoying, Han; Kloeden, Peter E.; Kloeden, Peter E. (John Wiley & Sons, 20150312)
Chemostat refers to a laboratory device used for growing microorganisms in a cultured environment, and has been regarded ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Xiaodi, Li; Xiaodi, Li; Rakkiyappan, R.; Rakkiyappan, R.; Xiaoying, Han; Xiaoying, Han (20150101)
In this paper, the stability problem of impulsive functional differential equations with infinite delays is considered. ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Herrera Cobos, Marta; Herrera Cobos, Marta; Marín Rubio, Pedro; Marín Rubio, Pedro (Pergamon Press, 20150101)
This paper is devoted to study the asymptotic behavior of a timedependent parabolic equation with nonlocal diffusion and ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato (Natural Sciences Publishing Corporation, 20150101)
We consider the effects of additive and multiplicative noise on the asymptotic behavior of a fourth order parabolic equation ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Xiaoying, Han; Xiaoying, Han; Kloeden, Peter E.; Kloeden, Peter E. (Society for Industrial and Applied Mathematics, 20150101)
The appearance of delay terms in a chemostat model can be fully justified since the future behavior of a dynamical system ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Xiaoying, Han; Xiaoying, Han; Kloeden, Peter E.; Kloeden, Peter E.; Rapaport, Alain; Rapaport, Alain (20150101)
Chemostat models have a long history in the biological sciences as well as in biomathematics. Hitherto most investigations ...

Article
Diop, Mamadou Abdoul; Diop, Mamadou Abdoul; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Ndiaye, Abdoul Aziz; Ndiaye, Abdoul Aziz (Taylor & Francis Inc., 20150101)
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 nondelay part generates a C0semigroup.

Presentation
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (20150101)

Article
Diop, Mamadou Abdoul; Diop, Mamadou Abdoul; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Institute of Mathematical Statistics, 20150101)
This paper is concerned with the existence and asymptotic stability in the \,pth moment of mild solutions of nonlinear ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Márquez Durán, Antonio Miguel; Márquez Durán, Antonio Miguel; Rivero Garvía, Luis Felipe; Rivero Garvía, Luis Felipe (20150101)
In this paper, it is analyzed a nonclassical nonautonomous di_usion equation with delay. First, the wellposedness and ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Morillas Jurado, Francisco; Morillas Jurado, Francisco; Valero Cuadra, José; Valero Cuadra, José (De Gruyter Open, 20150101)
In this paperwe study a nonautonomous lattice dynamical system with delay. Under rather general growth and dissipative ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Hammami, Mohamed Ali; Hammami, Mohamed Ali; Mchiri, Lassaad; Mchiri, Lassaad (Springer  Verlag Italia Srl, 20150101)
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.

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Xiaoying, Han; Xiaoying, Han; Kloeden, Peter E.; Kloeden, Peter E. (Natural Sciences Publishing Corporation, 20150101)
Traditional assumptions in the simple chemostat model include fixed availability of the nutrient and its supply rate, and ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Xiaoying, Han; Xiaoying, Han (20150101)
In this survey paper we review several aspects related to NavierStokes models when some hereditary characteristics ...

Article
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 (20150101)
In this paper we describe some dynamical properties of a Morse decomposition with a countable number of sets. In particular, ...

PhD Thesis
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Jara Pérez, Juan Carlos; Jara Pérez, Juan Carlos (20140321)
El estudio de los sistemas dinámicos es de gran importancia, ya que están relacionados con fenómenos del mundo real. Los ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Hammami, Mohamed Ali; Hammami, Mohamed Ali; Mchiri, Lassaad; Mchiri, Lassaad (20140101)
In this paper we establish some su cient conditions ensuring almost sure practical asymptotic stability with a nonexponential decay rate for solutions to stochastic evolution equations based on Lyapunov techniques.

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Colucci, Renato; Colucci, Renato (20140101)
We prove the existence of a pullback attractor for a non{autonomous fourth order evolution equation arising in the fi eld ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Diop, Mamadou Abdoul; Diop, Mamadou Abdoul; Ndoye, Ahmet Seyni; Ndoye, Ahmet Seyni (Research India Publications, 20140101)
In this paper, we study the existence and asymptotic stability in the pthmoment of mild solutions of nonlinear impulsive ...

Article
Anguiano Moreno, María; Anguiano Moreno, María; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (20140101)
The so called Lorenz84 model has been used in climatological studies, for example by coupling it with a lowdimensional ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Morillas Jurado, Francisco; Morillas Jurado, Francisco; Valero Cuadra, José; Valero Cuadra, José (20140101)
In this paper we first prove a rather general theorem about existence of solutions for an abstract differential equation ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Diop, Mamadou Abdoul; Diop, Mamadou Abdoul; Ndiaye, Abdoul Aziz; Ndiaye, Abdoul Aziz (Euclidean Press, 20140101)
This article presents some results on existence and uniqueness of mild solutions to neutral stochastic functional evolution ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Shaikhet, Leonid; Shaikhet, Leonid (20140101)
The investigation of stability for hereditary systems is often related to the construction of Lyapunov functionals. The ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Morillas Jurado, Francisco; Morillas Jurado, Francisco; Valero Cuadra, José; Valero Cuadra, José (20140101)
In this paper we study the asymptotic behaviour of solutions of a lattice dynamical system of a logistic type. Namely, we ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Xiaoying, Han; Xiaoying, Han (International Press, 20140101)
In this paper we establish some sufficient conditions for the exponential stability of the stationary solution to a ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Diop, Mamadou Abdoul; Diop, Mamadou Abdoul; Ndiaye, Abdoul Aziz; Ndiaye, Abdoul Aziz (20140101)
This paper deals with the existence, uniqueness and asymptotic behavior of mild solutions to neutral stochastic
delay ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kiss, Gábor; Kiss, Gábor (20130101)
We study the long term dynamics of nonautonomous functional di fferential equations. Namely, we establish existence results ...

Article
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 (20130101)
We show that the stochastic flow generated by the 2dimensional Stochastic NavierStokes equations with rough noise on a ...

Article
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 (20130101)
We define (time dependent) Morsedecompositions for nonautonomous evolution processes (nonautonomous dynamical systems) ...

Article
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 (20130101)
This paper is devoted to the investigation of the dynamics of nonautonomous
differential equations. The description of ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Márquez Durán, Antonio Miguel; Márquez Durán, Antonio Miguel (20130101)
A nonclassical nonautonomous diffusion equation with delay is analyzed. First, we prove the existence and uniqueness of ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Cheban, David; Cheban, David (20130101)
The aim of this paper is to describe the structure of global attractors for infinitedimensional nonautonomous dynamical ...

Article
Anguiano Moreno, María; Anguiano Moreno, María; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José (20130101)
The main aim of this paper is to analyse the asymptotic behaviour of a nonautonomous integrodifferential
parabolic equation ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Diop, Mamadou Abdoul; Diop, Mamadou Abdoul (20130101)
This paper deals with the existence and uniqueness of mild solutions to neutral stochastic delay functional integrodi ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kiss, Gábor; Kiss, Gábor; Taniguchi, Takeshi; Taniguchi, Takeshi (20130101)
We establish the results on the existence of pullback attractors for nonautonomous functional
differential equations with ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E. (20130101)
The globally modified NavierStokes equations (GMNSE) were introduced by Caraballo, Kloeden & Real in 2006 and have been ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Morillas, F.; Morillas, F.; Valero, J.; Valero, J. (Elsevier, 20120416)
In this paper we study the asymptotic behavior of solutions of a
firstorder stochastic lattice dynamical system with a ...

Article
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 (20120101)
This paper is dedicated to estimate the fractal dimension of exponential global
attractors of some generalized gradientlike ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Morillas Jurado, Francisco; Morillas Jurado, Francisco; Valero Cuadra, José; Valero Cuadra, José (20120101)
In this paper we study the asymptotic behaviour of solutions of a firstorder stochastic lattice
dynamical system with an ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Liu, Zenxhin; Liu, Zenxhin (20120101)
In this paper we introduce the concept of a gradient random dynamical system as a random semiflow
possessing a continuous ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (20120101)

Article
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 (20120101)
The global attractor of a gradientlike semigroup has a Morse decomposition. Associated to this Morse decomposition there ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (20120101)

PhD Thesis
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José; Valero Cuadra, José; Valero Cuadra, José; Anguiano Moreno, María; Anguiano Moreno, María (20110901)
Este trabajo está dividido en cinco capítulos. En los Capítulos 1 y 3, se trata la parte teórica de los sistemas dinámicos ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Márquez Durán, Antonio Miguel; Márquez Durán, Antonio Miguel; Real Anguas, José; Real Anguas, José (20110101)
The longtime behaviour of a stochastic 3D LANS® model on a bounded domain is analysed. First, we reformulate the model ...

Article
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 (20110101)
In this paper we consider the strongly damped wave equation with time dependent terms
utt − u − γ(t) ut + β"(t)ut = f(u), ...

Article
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 (20110101)
In this paper we prove that gradientlike semigroups (in the sense of Carvalho and Langa (2009 J. Diff. Eqns 246 2646–68)) ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Cheban, David; Cheban, David (20110101)
The aim of this paper is to study the almost periodic and asymptotically almost periodic solutions on (0,+1) of the Li´enard ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; Taniguchi, Takeshi; Taniguchi, Takeshi (20110101)
In this paper we investigate the existence, uniqueness and exponential asymptotic behavior of mild solutions to stochastic ...

PhD Thesis
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Rivero Garvía, Luis Felipe; Rivero Garvía, Luis Felipe (20110101)
Este trabajo está dividido en dos partes. Una primera en la que se trata la parte teórica de los sistemas dinámicos autónomos ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real, José; Real, José; Márquez, Antonio M.; Márquez, Antonio M. (20100904)
We prove the existence and uniqueness of strong solutions of a threedimensional system of globally modified Navier–Stokes ...

Article
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 (20100101)
This paper is concerned with the existence of pullback attractors for evolution
processes. Our aim is to provide results ...

Article
Balibrea Gallego, Francisco; Balibrea Gallego, Francisco; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E.; Valero Cuadra, José; Valero Cuadra, José (20100101)
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.

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Cheban, David; Cheban, David (20100101)
We analyze the existence of almost periodic (respectively, almost automorphic, recurrent) solutions of a linear nonhomogeneous ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José; Márquez, Antonio M.; Márquez, Antonio M. (20100101)
We prove the existence and uniqueness of strong solutions of a threedimensional system of globally
modified Navier–Stokes ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; Schmalfuss, Björn; Schmalfuss, Björn; Valero Cuadra, José; Valero Cuadra, José (20100101)
In this work we present the existence and uniqueness of pullback and random attractors for stochastic evolution equations ...

Article
Anguiano Moreno, María; Anguiano Moreno, María; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José (20100101)
We prove some regularity results for the pullback attractor of a reactiondiffusion model. First we establish a general ...

Article
Anguiano Moreno, María; Anguiano Moreno, María; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José (20100101)

Article
Anguiano Moreno, María; Anguiano Moreno, María; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José; Valero Cuadra, José; Valero Cuadra, José (20100101)
The existence of a pullback attractor for a reactiondiffusion equations in an unbounded domain containing a nonautonomous ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; Schmalfuss, Björn; Schmalfuss, Björn; Valero Cuadra, José; Valero Cuadra, José (20100101)
The longtime behavior of an integrodifferential parabolic equation of diffusion type with memory terms, expressed by ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E. (20090101)
We show that infinitedimensional integrodifferential equations which involve an integral of the solution over the time ...

Article
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 (20090101)
In this paper we consider a dissipative damped wave equation with nonautonomous damping
of the form
utt + ¯(t)ut = ¢u + ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kiss, Gábor; Kiss, Gábor (20090101)
We establish some results on the existence of pullback attractors for nonautonomous delay di fferential equations with ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Márquez Durán, Antonio Miguel; Márquez Durán, Antonio Miguel; Real Anguas, José; Real Anguas, José (20090101)
We obtain some results on the existence and uniqueness, and exponential stability of solutions for the threedimensional ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Cheban, David; Cheban, David (20090101)
The wellknown Favard's theorem states that the linear differential equation
x′=A(t)x+f(t)
Turn MathJax on
with Bohr ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Cheban, David; Cheban, David (20090101)
In this paper we continue the research started in a previous paper, where we proved that the linear differential equation
(1) ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; Schmalfuss, Björn; Schmalfuss, Björn; Valero Cuadra, José; Valero Cuadra, José (20080101)
We first prove the existence and uniqueness of pullback and random attractors for abstract multivalued nonautonomous and ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E.; Neuenkirch, Andreas; Neuenkirch, Andreas (20080101)
The synchronization of Stratonovich stochastic di erential equations (SDE) with a onesided dissipative Lipschitz drift ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Chueshov, Igor D.; Chueshov, Igor D.; Real Anguas, José; Real Anguas, José (20080101)
We study the asymptotic behaviour of a nonautonomous stochastic reactiondiffusion equation with memory. In fact, we prove ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Lu, Kening; Lu, Kening (20080101)
In this paper, we consider a stochastic lattice di®erential equation with di®usive nearest
neighbor interaction, a dissipative ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E.; Real Anguas, José; Real Anguas, José (20080101)
We obtain regularity results for solutions of the three dimensional system of globally modified NavierStokes equations, ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Valero Cuadra, José; Valero Cuadra, José (20080101)
We prove that the asymptotic behaviour of partial differential inclusions and partial differential equations without ...

Presentation
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; Schmalfuss, Björn; Schmalfuss, Björn; Valero Cuadra, José; Valero Cuadra, José (20070901)
En primer lugar probamos la existencia y unicidad de atractor para sistemas
dinámicos multivaluados abstractos, tanto en ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E.; Marín Rubio, Pedro; Marín Rubio, Pedro (20070101)
The upper semicontinuous convergence of approximate attractors for an infinite delay differential equation of logistic ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Marín Rubio, Pedro; Marín Rubio, Pedro; Valero Cuadra, José; Valero Cuadra, José (Elsevier, 20070101)
We prove the existence of attractors for some types of differential problems containing infinite delays. Applications and ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José; Shaikhet, Leonid; Shaikhet, Leonid (20070101)
Stability investigation of hereditary systems often is connected with the construction of Lyapunov functionals. The general ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Chueshov, Igor D.; Chueshov, Igor D.; Marín Rubio, Pedro; Marín Rubio, Pedro; Real Anguas, José; Real Anguas, José (20070101)
The existence and uniqueness of solutions for a stochastic reactiondiffusion equation with infinite delay is proved. ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; Schmalfuss, Björn; Schmalfuss, Björn (20070101)
We consider the exponential stability of semilinear stochastic evolution equations with delays when zero is not a solution ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Cheban, David; Cheban, David (20070101)
The aim of this paper is to prove the existence of Levitan/Bohr almost periodic, almost automorphic, recurrent and Poisson ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José; Taniguchi, Takeshi; Taniguchi, Takeshi (20070101)
In this paper we analyse the almost sure exponential stability and ultimate boundedness of the solutions to a class of ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Chueshov, Igor D.; Chueshov, Igor D.; Kloeden, Peter E.; Kloeden, Peter E. (20070101)
A system of semilinear parabolic stochastic partial differential equations with additive
spacetime noise is considered ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Sociedad Española de Matemática Aplicada, 20061201)
This paper is intended to be a brief review on some recent results
on the stabilization effect produced by noise in phenomena ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E.; Real Anguas, José; Real Anguas, José (20060101)
We prove the existence of a stationary random solution to a delay random ordinary differential system which attracts all ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio (20060101)
In this paper, we point out the different longtime behaviour of stochastic partial differential equations when one considers ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Márquez Durán, Antonio Miguel; Márquez Durán, Antonio Miguel; Real Anguas, José; Real Anguas, José (20060101)
We analyse the asymptotic behaviour of a 3D Lagrangian averaged NavierStokes model (3D LANS) with delays. In fact, we ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E.; Marín Rubio, Pedro; Marín Rubio, Pedro (20060101)
We investigate the asymptotic behaviour of a general setvalued skew product flow (SVSPF), that is, a setvalued cocycle ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Crauel, Hans; Crauel, Hans; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Robinson, James C.; Robinson, James C. (20060101)
We investigate the effect of perturbing the ChafeeInfante scalar reaction diffusion equation, ut−Δu = βu−u3, by noise. ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E. (20060101)
Under a onesided dissipative Lipschitz condition on its drift, a stochastic evolution equation with additive noise of the ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Lukaszewicz, Grzegorz; Lukaszewicz, Grzegorz; Real Anguas, José; Real Anguas, José (20060101)
First, we introduce the concept of pullback asymptotically compact nonautonomous dynamical system as an extension of the ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Lukaszewicz, Grzegorz; Lukaszewicz, Grzegorz; Real Anguas, José; Real Anguas, José (20060101)
In this Note we first introduce the concept of pullback asymptotic compactness. Next, we establish a result ensuring the ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E.; Schmalfuss, Björn; Schmalfuss, Björn (20060101)
We investigate the existence, uniqueness and exponential stability of nonconstant stationary solutions of stochastic ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; Real Anguas, José; Real Anguas, José (20060101)
Sufficient conditions for exponential mean square stability of solutions to delayed stochastic partial differential equations ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José; Taniguchi, Takeshi; Taniguchi, Takeshi (20060101)
We prove existence and uniqueness of solutions for a stochastic version of the 3DLagrangian
averaged NavierStokes (LANS®) ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Valero Cuadra, José; Valero Cuadra, José (20050101)
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

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Valero Cuadra, José; Valero Cuadra, José (20050101)
We introduce the concept of a monotone multivalued semi ow as an orderpreserving map. This
de nition is motivated by ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Chueshov, Igor D.; Chueshov, Igor D.; Langa Rosado, José Antonio; Langa Rosado, José Antonio (20050101)
An abstract system of coupled nonlinear parabolichyperbolic partial differential equations subjected to additive white ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Márquez Durán, Antonio Miguel; Márquez Durán, Antonio Miguel; Real Anguas, José; Real Anguas, José (20050101)
Existence and uniqueness of solutions for a stochastic version of the 3DLagrangian averaged NavierStokes (LANS®) equation in a bounded domain and containing some hereditary characteristics are proved.

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Marín Rubio, Pedro; Marín Rubio, Pedro; Valero Cuadra, José; Valero Cuadra, José (20050101)
The asymptotic behaviour of some types of retarded differential equations, with both variable and distributed delays, is ...

PhD Thesis
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José; Márquez Durán, Antonio Miguel; Márquez Durán, Antonio Miguel (20050101)
"Como es bien conocido, las ecuaciones de NavierStokes gobiernan el movimiento de fluidos comunes como el agua, el aire, ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E. (20050101)
It is shown that the synchronization of dissipative systems persists when they are disturbed by additive noise no matter ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José (20040101)
The existence of an attractor for a 2DNavierStokes system with delay is proved. The theory of pullback attractors is ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E.; Schmalfuss, Björn; Schmalfuss, Björn (20040101)
We consider the exponential stability of stochastic evolution equations with Lipschitz continuous nonlinearities when ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Robinson, James C.; Robinson, James C. (20040101)
Some results concerning the stability and stabilisation of stochastic linear partial differential equations in the sense ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E.; Real Anguas, José; Real Anguas, José (20040101)
The existence of a pullback (and also a uniform forward) attractor is proved for a damped wave equation containing a delay ...

PhD Thesis
Real Anguas, José; Real Anguas, José; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Marín Rubio, Pedro; Marín Rubio, Pedro (20030523)
La memoria está compuesta de dos partes: la primera se enmarca dentro del Análisis Estocástico y la segunda parte en la ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José (20030101)
Some results on the asymptotic behaviour of solutions to NavierStokes equations when the external force contains some ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; Real Anguas, José; Real Anguas, José (20030101)
Some results on the pathwise asymptotic stability of solutions to stochastic partial differential equations are proved. ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Valero Cuadra, José; Valero Cuadra, José (20030101)
Some results on the relationship of the solutions of a stochastic di erential inclusion and the corresponding random di ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Valero Cuadra, José; Valero Cuadra, José (20030101)
The concept of nonautonomous (or cocycle) attractor has become a proper tool for the study of the asymptotic behaviour of ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Marín Rubio, Pedro; Marín Rubio, Pedro; Robinson, James C.; Robinson, James C. (20030101)
This paper presents a comparison between two abstract frameworks
in which one can treat multivalued semiflows and their ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; Real Anguas, José; Real Anguas, José (20030101)
Sufficient conditions for exponential mean square stability of solutions to delayed stochastic partial differential equations ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Kloeden, Peter E.; Kloeden, Peter E.; Marín Rubio, Pedro; Marín Rubio, Pedro (20030101)
Weak pullback attractors are de ned for nonautonomous setvalued processes and their existence and upper semi continuous ...

Article
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 (20030101)
In this paper we study the existence of pullback global attractors for multivalued processes generated
by differential ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; Real Anguas, José; Real Anguas, José (20030101)
Some sufficient conditions concerning stability of solutions of stochastic differential evolution equations with general ...

PhD Thesis
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José; Garrido Atienza, María José; Garrido Atienza, María José (20020101)

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Taniguchi, Takeshi; Taniguchi, Takeshi (20020101)
Some results on the pathwise exponential stability of the weak solutions to a stochastic 2DNavierStokes equation are ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Garrido Atienza, María José; Garrido Atienza, María José; Real Anguas, José; Real Anguas, José (20020101)
Some results on the existence and uniqueness of solutions for stochastic evolution equations
containing some hereditary ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Valero Cuadra, José; Valero Cuadra, José (20020101)
We introduce the concept of multivalued random dynamical system (MRDS) as a measurable multivalued flow satisfying the ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (20010101)
Some results on the asymptotic behaviour of solutions of diff erential equations concerning general decay rate are proved. ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Cuadra Valero, José; Cuadra Valero, José (20010101)
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
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Valero Cuadra, José; Valero Cuadra, José (Masaryk University, 20010101)
The concept of global attractor for stochastic partial differential inclusions has been recently introduced as a joint ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José (20010101)
Some results on the existence and uniqueness of solutions to NavierStokes equations when the external force contains some hereditary characteristics are proved.

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Valero Cuadra, José; Valero Cuadra, José (20010101)
We introduce the concept of multivalued random dynamical system (MRDS) as a measurable
multivalued flow satisfying the ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Liu, Kai; Liu, Kai; Mao, Xuerong; Mao, Xuerong (20010101)
Some results on stabilization of (deterministic and stochastic) partial differential equations are established. In particular, ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Robinson, James C.; Robinson, James C. (20010101)
We study in some detail the structure of the random attractor for the Chafee{Infante
reaction{di¬usion equation perturbed ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Robinson, James C.; Robinson, James C. (20010101)
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.

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (20010101)
Existence and uniqueness of solutions for a class of nonlinear functional differential equations in Hilbert spaces are ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Liu, Kai; Liu, Kai (20010101)
The main objective of this paper is to investigate the asymptotic stability for diffusion processes driven by a class of ...

Article
Anguiano Moreno, María; Anguiano Moreno, María; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José (20010101)
Some exponential growth results for the pullback attractor of a reactiondiffusion
when time goes to ¡1 are proved in this ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Robinson, James C.; Robinson, James C. (20000101)
We study the asymptotic behaviour of a reactiondiffusion equation, and prove that the addition of multiplicative white ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Liu, Kai; Liu, Kai (20000101)
Existence and uniqueness of strong solutions for a class of stochastic functional di fferential equations in Hilbert spaces ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Liu, Kai; Liu, Kai (19990101)
Some criteria for the mean square and almost sure exponential stability of nonlinear stochastic partial differential ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio (19990101)
The theory of random attracting sets highlights interesting properties of the asymptotic behaviour of some stochastic ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Liu, Kai; Liu, Kai (19990101)
A semilinear stochastic partial differential equation with variable delays is considered. Sufficient conditions for the ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio; Robinson, James C.; Robinson, James C. (19980101)
The relationship between random attractors and global attractors for dynamical systems is studied. If a partial differential ...

PhD Thesis
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Langa Rosado, José Antonio (19980101)
"En el Capítulo 1, presentamos una síntesis de los resultados básicos sobre atractores globales que pueden encontrarse en ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José (19940101)
Sufficient conditions to get exponential stability for the sample paths (with probability one) of a nonlinear monotone ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás; Real Anguas, José; Real Anguas, José (19930101)
We consider a stochastic non–linear Partial Differential Equation with delay which may be regarded as a perturbed equation. ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (19910101)
The main aim of this paper is to study stochastic PDE's with delay terms. In fact, we prove existence and uniqueness of ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (19910101)
We state some results on existence and uniqueness for the solution of non linear stochastic PDEs
with deviating arguments. ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (19900101)
Sufficient conditions for pathwise asymptotic exponential stability of the solution of the stochastic PDE with delay d x ...

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (Universidad de Extremadura, 19890101)

Article
Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (19880101)
Sufficient conditions for pathwise exponential stability of the zero solution of stochastic PDE with deviating argument ...

PhD Thesis
Real Anguas, José; Real Anguas, José; Caraballo Garrido, Tomás; Caraballo Garrido, Tomás (19880101)
"En esta memoria presentamos una contribución al estudio de la estabilidad en la Ecuaciones en Derivadas Parciales ...
