Data

NameCaraballo Garrido, Tomás
DepartmentEcuaciones Diferenciales y Análisis Num.
Knowledge areaAnálisis Matemático
Professional categoryCatedrático de Universidad
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  Publications

 

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Corrigendum to the paper: A way to model stochastic perturbations in population dynamics models with bounded realizations. Commun Nonlinear Sci Numer Simulat, 77 (2019), 239–257

Caraballo Garrido, Tomás; Colucci, Renato; López de la Cruz, Javier; Rapaport, Alain (Elsevier [Commercial Publisher], 2021-05-01)
In this corrigendum we correct an error in our paper [T. Caraballo, R. Colucci, J. López-de-la-Cruz and A. Rapaport. A way ...
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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, 2021-02-04)
This paper investigates a chemostat model with wall growth and Haldane consumption kinetics. In addition, bounded random ...
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Statistical solution and Liouville type theorem for the Klein-Gordon-Schrödinger equations

Zhao, Caidi; Caraballo Garrido, Tomás; Lukaszewicz, Grzegorz (Elsevier [Commercial Publisher], Academic Press [Associate Organisation], 2021-01-28)
In this article, the authors investigate the system of Schr odinger and Klein-Gordon equations with Yukawa coupling. They ...
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Pullback exponential attractors for differential equations with delay

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

Caraballo Garrido, Tomás; Carvalho, Alexandre Nolasco; Langa Rosado, José Antonio; Oliveira Sousa, Alexandre N. (ScienceDirect, 2021-01-01)
In this work, we study permanence of hyperbolicity for autonomous differential equations under nonautonomous random/stochastic ...
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Dynamics and numerical simulations to predict empirical antibiotic treatment of multi-resistant Pseudomonas aeruginosa infection

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

Wang, Jintao; Zhao, Caidi; Caraballo Garrido, Tomás (Elsevier, 2020-12-01)
This article investigates the three-dimensional globally modified Navier-Stokes equations with unbounded variable delays. ...
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Study of the chemostat model with non-monotonic growth under random disturbances on the removal rate

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

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

Xu, Jiaohui; Zhang, Zhengce; Caraballo Garrido, Tomás (Elsevier [Commercial Publisher], Academic Press [Associate Organisation], 2020-09-15)
The paper addresses a kind of non-autonomous nonlocal parabolic equations when the external force contains hereditary ...
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Morse decomposition for gradient-like multi-valued autonomous and nonautonomous dynamical systems

Wang, Yejuan; Caraballo Garrido, Tomás (American Institute of Mathematical Sciences (AIMS), 2020-08-01)
In this paper, we first prove that the property of being a gradientlike general dynamical system and the existence of a ...
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Long time dynamics for functional three-dimensional Navier-Stokes-Voigt equations

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

NGuyen, Huy Tuan; Caraballo Garrido, Tomás (American Mathematical Society, 2020-06-11)
In this paper, we consider fractional nonclassical diffusion equations under two forms: initial value problem and terminal ...
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A free boundary tumor model with time dependent nutritional supply

Sun, Wenlong; Caraballo Garrido, Tomás; Han, Xiaoying; Kloeden, Peter E. (Elsevier, 2020-06-01)
A non-autonomous free boundary model for tumor growth is studied. The model consists of a nonlinear reaction diffusion ...
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Trajectory statistical solutions and Liouville type equations for evolution equations: abstract results and applications

Zhao, Caidi; Li, Yanjiao; Caraballo Garrido, Tomás (Elsevier, 2020-06-01)
In this article, we first prove, from the viewpoint of infinite dynamical system, sufficient conditions ensuring the ...
PhD Thesis
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A contribution to the analysis of time fractional stochastic functional partial differential equations and applications

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

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

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

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

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

Caraballo Garrido, Tomás; Ogouyandjou, Carlos; Allognissode, Fulbert Kuessi; Diop, Mamadou Abdoul (American Institute of Mathematical Sciences (AIMS), 2020-02-01)
The existence and uniqueness of mild solution of an impulsive stochastic system driven by a Rosenblatt process is analyzed ...
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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, 2020-01-01)
In this article we analyze the randomized non-autonomous Bertalanffy model x 0 (t, ω) = a(t, ω)x(t, ω) + b(t, ω)x(t, ω) 2/3, ...
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Existence of periodic positive solutions to a nonlinear Lotka-Votlerra competition systems

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

Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Valero Cuadra, José (Springer, 2020-01-01)
In this paper we establish a strong comparison principle for a nonautonomous differential inclusion with a forcing term ...
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Stability results for neutral stochastic functional differential equations via fixed point methods

Benhadri, Mimia; Caraballo Garrido, Tomás; Zeghdoudi, Halim (Taylor and Francis, 2020-01-01)
In this paper we prove some results on the mean square asymptotic stability of a class of neutral stochastic differential ...
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Minimizing the expected time to detect a randomly located lost target using 3-dimensional search technique

Caraballo Garrido, Tomás; Teamah, Abd El-Moneim Anwar; El-Bagoury, Abd Al-Aziz Hosni (Taylor and Francis, 2020-01-01)
This paper considers a new model in search theory to find a randomly located target in the 3-dimensional space. An ...
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Strong trajectory statistical solutions and Liouville type equation for dissipative Euler equations

Zhao, Caidi; Song, Zhongchun; Caraballo Garrido, Tomás (Elsevier, 2020-01-01)
The main aim of this letter is to use the strong compact strong trajectory attractor to construct the strong trajectory ...
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Upper and Lower Semicontinuity of Impulsive Cocycle Attractors for Impulsive Nonautonomous Systems

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

Liu, Linfang; Caraballo Garrido, Tomás (Springer, 2019-12-01)
Some results concerning a stochastic 2D Navier-Stokes system when the external forces contain hereditary characteristics ...
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On the asymptotic behavior of highly nonlinear hybrid stochastic delay differential equations

Zhang, Tian; Chen, Huabin; Yuan, Chenggui; Caraballo Garrido, Tomás (American Institute of Mathematical Sciences, 2019-10-01)
In this paper, under a local Lipschitz condition and a monotonicity condition, the problems on the existence and uniqueness ...
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A way to model stochastic perturbations in population dynamics models with bounded realizations

Caraballo Garrido, Tomás; Colucci, Renato; López de la Cruz, Javier; Rapaport, Alain (Elsevier, 2019-10-01)
In this paper, we analyze the use of the Ornstein-Uhlenbeck process to model dynamical systems subjected to bounded noisy ...
PhD Thesis
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Resolubility of linear Cauchy problems on Fréchet spaces and a delayed Kaldor’s model

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

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

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

Samprogna, Rodrigo Antonio; Gentile Mossa, Claudia Buttarello; Caraballo Garrido, Tomás; Schiabel, Karina (American Institute of Mathematical Sciences, 2019-08-01)
In this work the theory of generalized processes is used to describe the dynamics of a nonautonomous multivalued problem ...
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Modeling and analysis of random and stochastic input flows in the chemostat model

Caraballo Garrido, Tomás; Garrido Atienza, María José; López de la Cruz, Javier (American Institute of Mathematical Sciences, 2019-08-01)
In this paper we study a new way to model noisy input flows in the chemostat model, based on the Ornstein-Uhlenbeck process. ...
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Well-posedness and dynamics of impulsive fractional stochastic evolution equations with unbounded delay

Xu, Jiaohui; Zhang, Zhengce; Caraballo Garrido, Tomás (Elsevier, 2019-08-01)
This paper is concerned with the well-posedness and dynamics of delay impulsive fractional stochastic evolution equations ...
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Global stability and positive recurrence of a stochastic SIS model with Lévy noise perturbation

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

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

Xu, Jiahoui; Caraballo Garrido, Tomás (American Institute of Mathematical Sciences, 2019-06-01)
This paper is first devoted to the local and global existence of mild solutions for a class of fractional impulsive ...
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The asymptotic behaviour of fractional lattice systems with variable delay

Liu, Linfang; Caraballo Garrido, Tomás; Kloeden, Peter E. (De Gruyter, 2019-06-01)
The existence and uniqueness of global solutions for a fractional functional differential equation is established. The ...
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Asymptotic regularity of trajectory attractor and trajectory statistical solution for the 3D globally modified Navier-Stokes equations

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

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

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

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

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

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

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

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

Caraballo Garrido, Tomás; Herrera Cobos, Marta; Marín Rubio, Pedro (Cambridge University Press, 2018-10-01)
In this paper, the existence and uniqueness of weak and strong solutions for a non-autonomous nonlocal reaction-diffusion ...
PhD Thesis
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Analysis of infinite dimensional dynamical systems associated to functional differential equations.

Caraballo Garrido, Tomás; Liu, Linfang (2018-06-28)
Based on the theory of functional diferential equations, theory of semigroup, theory of random dynamical systems and theory ...
PhD Thesis
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Sistemas dinámicos en modelos estocásticos con ruido fraccionario.

Caraballo Garrido, Tomás; Garrido Atienza, María José; López de la Cruz, Javier (2018-06-28)
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Robustness of time-dependent attractors in H1-norm for nonlocal problems

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

Caraballo Garrido, Tomás; Herrera Cobos, Marta; Marín Rubio, Pedro (Elsevier, 2018-03-01)
In this paper, we focus on studying the existence of attractors in the phase spaces L2(Ω) and Lp(Ω) (among others) for ...
Final Degree Project
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Aplicación de los sistemas diferenciales al estudio de un modelo epidemiológico con reinfección

Caraballo Garrido, Tomás; Lindes Colón, Mercedes (2018-01-01)
Mathematical modeling, currently, is a very important element in health system, since it allows studying the incidence, ...
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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, 2018-01-01)
This work is devoted to investigate the existence and uniqueness of a global positive solution for a stochastic epidemic ...
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Dynamics of a continuous Hénon model

Caraballo Garrido, Tomás; Colucci, Renato; Guerrini, Luca (Wiley, 2018-01-01)
We study a continuous Hénon system obtained by considering the discrete original model in continuous time. While the ...
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Dynamic evolution of a hydraulic-mechanical-electric system with randomly fluctuating speed based on Chebyshev polynomial approximation method

Xu, Beibei; Chen, Diyi; Caraballo Garrido, Tomás (Springer, 2018-01-01)
The research proposed in this paper focuses on the dynamic evolution of a hydraulic-mechanical-electric system under the ...
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On a predator prey model with nonlinear harvesting and distributed delay

Caraballo Garrido, Tomás; Colucci, Renato; Guerrini, Luca (American Institute of Mathematical Sciences, 2018-01-01)
A predator prey model with nonlinear harvesting (Holling type-II) with both constant and distributed delay is considered. ...
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Pullback attractor for a dynamic boundary non-autonomous problem with Infinite delay

Samprogna, Rodrigo Antonio; Caraballo Garrido, Tomás (American Institute of Mathematical Sciences, 2018-01-01)
In this work we prove the existence of solution for a p-Laplacian non-autonomous problem with dynamic boundary and infinite ...
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A stochastic SIRI epidemic model with Lévy noise

Berrhazi, Badr-eddine; El Fatini, Mohamed; Caraballo Garrido, Tomás; Pettersson, Roger (American Institute of Mathematical Sciences, 2018-01-01)
Some diseases such as herpes, bovine and human tuberculosis exhibit relapse in which the recovered individuals do not ...
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Analysis of a stochastic SIR model with fractional Brownian motion

Caraballo Garrido, Tomás; Keraani, Sami (Taylor & Francis, 2018-01-01)
In this article, a stochastic version of a SIR nonautonomous model previously introduced in Kloeden and Kozyakin (2011) ...
Presentation
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Pullback attractors to analyze the effect of random and stochastic disturbances in the chemostat model

López de la Cruz, Javier; Caraballo Garrido, Tomás; Garrido Atienza, María José; Rapaport, Alain (2018-01-01)
In this talk, some random and stochastic disturbances in the chemostat model will be analyzed by making use of the modern ...
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Random pullback exponential attractors: general existence results for random dynamical systems in Banach spaces

Caraballo Garrido, Tomás; Sonner, Stefanie (American Institute of Mathematical Sciences, 2017-12-01)
We derive general existence theorems for random pullback exponential attractors and deduce explicit bounds for their fractal dimension. The results are formulated for asymptotically compact random dynamical systems in Banach spaces.
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Practical exponential stability of impulsive stochastic functional differential equations

Caraballo Garrido, Tomás; Hammami, Mohamed Ali; Mchiri, Lassaad (Elsevier, 2017-11-01)
This paper is devoted to the investigation of the practical exponential stability of impulsive stochastic functional ...
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Dynamics of a class of ODEs via wavelets

Munhoz Rodrigues, Hildebrando; Caraballo Garrido, Tomás; Fuzeto Gameiro, Marcio (American Institute of Mathematical Sciences, 2017-11-01)
The objective of this paper is to study a perturbed linear hyperbolic differential equation. The first part of this work ...
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Well-posedness and dynamics of a fractional stochastic integro-differential equation

Liu, Linfang; Caraballo Garrido, Tomás (Elsevier, 2017-09-15)
In this paper we investigate the well-posedness and dynamics of a fractional stochastic integro-differential equation ...
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Long time behavior of stochastic parabolic problems with white noise in materials with thermal memory

Liu, Linfang; Caraballo Garrido, Tomás; Kloeden, Peter E. (Springer, 2017-09-01)
The existence and limiting behavior of the solutions of stochastic parabolic problems with thermal memory are investigate ...
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Stochastic differential equations with non-instantaneous impulses driven by a fractional Brownian motion

Boudaoui, Ahmed; Caraballo Garrido, Tomás (American Institute of Mathematical Sciences, 2017-09-01)
This paper is concerned with the existence and continuous dependence of mild solutions to stochastic differential equations ...
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Dynamics of some stochastic chemostat models with multiplicative noise

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

Blouhi, Tayeb; Caraballo Garrido, Tomás; Ouahab, Abdelghani (Taylor & Francis, 2017-08-01)
In this paper we correct an error made in our paper [Blouhi, T.; Caraballo, T.; Ouahab, A. Existence and stability results ...
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Attractors for a random evolution equation with infinite memory: Theoretical results

Caraballo Garrido, Tomás; Garrido Atienza, María José; Schmalfuss, Björn; Valero Cuadra, José (American Institute of Mathematical Sciences, 2017-07-01)
The long-time behavior of solutions (more precisely, the existence of random pullback attractors) for an integro-differential ...
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Global attractor for a nonlocal p-Laplacian equation without uniqueness of solution

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

Caraballo Garrido, Tomás; Márquez Durán, Antonio Miguel; Rivero Garvía, Luis Felipe (American Institute of Mathematical Sciences, 2017-07-01)
We show existence and uniqueness of solutions for a non-classical and non-autonomous diffusion equation with infinite delay ...
Final Degree Project
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Ecuaciones diferenciales con retardo: Aplicación a un modelo de quimiostato

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

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

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

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

Caraballo Garrido, Tomás; Colucci, Renato (Wiley, 2017-02-01)
In this paper we analyze a model presenting formation of microstructure depending on the parameters and the initial data. ...
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Pullback, forward and chaotic dynamics in 1-D non-autonomous linear-dissipative equations

Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Obaya García, Rafael (IOP Publishing, 2017-01-01)
The global attractor of a skew product semiflow for a non-autonomous differential equation describes the asymptotic behaviour ...
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A comparison between random and stochastic modeling for a SIR model

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

Liu, Linfang; Caraballo Garrido, Tomás; Fu, Xianlong (International Press, 2017-01-01)
We first study the well-posedness of a non-autonomous incompressible non-Newtonian fluid with delay. The existence of ...
Presentation
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Random dynamical systems to analyze different ways of modeling stochastic chemostats

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

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

Caraballo Garrido, Tomás; Carvalho, Alexandre Nolasco; Barbosa da Costa, Henrique; Langa Rosado, José Antonio (American Institute of Mathematical Sciences, 2016-11-01)
In this paper we prove the equivalence between equi-attraction and continuity of attractors for skew-product semi-flows, ...
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Impulsive surfaces on dynamical systems

Bonotto, Everaldo de Mello; Bortolan, Matheus Cheque; Caraballo Garrido, Tomás; Collegari, Rodolfo (Springer, 2016-10-01)
This work is devoted to the construction of impulsive sets in Rn. In the literature, there are many examples of impulsive ...
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Non-autonomous dynamics of a semi-Kolmogorov population model with periodic forcing

Caraballo Garrido, Tomás; Colucci, Renato; Han, Xiaoying (Elsevier, 2016-10-01)
In this paper we study a semi-Kolmogorov type of population model, arising from a predator-prey system with indirect ...
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Mild solutions of non-Lipschitz stochastic integrodifferential evolution equations

Diop, Mamadou Abdoul; Caraballo Garrido, Tomás; Mané, Aziz (Wiley, 2016-10-01)
In this work we study the existence and uniqueness of mild solutions for stochastic partial integrodifferential equations ...
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Semi-Kolmogorov models for predation with indirect effects in random environments

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

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

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

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

Blouhi, Tayeb; Caraballo Garrido, Tomás; Ouahab, Abdelghani (Taylor & Francis, 2016-01-01)
Some results on the existence and uniqueness of mild solution for a system of semilinear impulsive differential equations ...
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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, 2016-01-01)
In this paper, we prove the local and global existence and attractivity of mild solutions for stochastic impulsive neutral functional differential equations with infinite delay, driven by fractional Brownian motion.
Chapter of Book
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Some aspects concerning the dynamics of stochastic chemostats

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

Caraballo Garrido, Tomás; Han, Xiaoying (Springer, 2016-01-01)
Chapter of Book
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A random model for immune response to virus in fluctuating environments

Sadovnichiy, Victor A.; Zgurovsky, Mikhail Z.; Asai, Yusuke; Caraballo Garrido, Tomás; Han, Xiaoying; Kloeden, Peter E. (Springer, 2016-01-01)
In this work we study a model for virus dynamics with a random immune response and a random production rate of susceptible ...
Presentation
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A survey on impulsive dynamical systems

Bonotto, Everaldo de Mello; Bortolan, Matheus Cheque; Caraballo Garrido, Tomás; Collegari, Rodolfo (Bolyai Institute (University of Szeged), 2016-01-01)
In this survey we provide an introduction to the theory of impulsive dynamical systems in both the autonomous and nonautonomous ...
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Random attractors for stochastic lattice dynamical systems with infinite multiplicative white noise

Caraballo Garrido, Tomás; Xiaoying, Han; Schmalfuss, Björn; Valero Cuadra, José (2016-01-01)
In this paper we investigate the long term behavior of a stochastic lattice dynamical system with a diffusive nearest ...
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New trends on nonlinear dynamics and its applications

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

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

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

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

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

Caraballo Garrido, Tomás; Xiaoying, Han; Kloeden, Peter E. (John Wiley & Sons, 2015-03-12)
Chemostat refers to a laboratory device used for growing microorganisms in a cultured environment, and has been regarded ...
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Exponential behavior of solutions to stochastic integrodifferential equations with distributed delays

Diop, Mamadou Abdoul; Caraballo Garrido, Tomás; Ndiaye, Abdoul Aziz (Taylor & Francis Inc., 2015-01-01)
In this work, we study the existence, uniqueness, and exponential asymptotic behavior of mild solutions to stochastic integrodifferential delay evolution equations. We assume that the non-delay part generates a C0-semigroup.
Presentation
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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, 2015-01-01)
We consider the effects of additive and multiplicative noise on the asymptotic behavior of a fourth order parabolic equation ...
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A survey on Navier-Stokes models with delays: Existence, uniqueness and asymptotic behavior of solutions

Caraballo Garrido, Tomás; Xiaoying, Han (2015-01-01)
In this survey paper we review several aspects related to Navier-Stokes models when some hereditary characteristics ...
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Asymptotic stability of neutral stochastic functional integro-differential equations with impulses

Diop, Mamadou Abdoul; Caraballo Garrido, Tomás (Institute of Mathematical Statistics, 2015-01-01)
This paper is concerned with the existence and asymptotic stability in the \,p-th moment of mild solutions of nonlinear ...
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Practical exponential stability in mean square of stochastic partial differential equations

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

Caraballo Garrido, Tomás; Xiaoying, Han; Kloeden, Peter E.; Rapaport, Alain (2015-01-01)
Chemostat models have a long history in the biological sciences as well as in biomathematics. Hitherto most investigations ...
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On the stability of impulsive functional differential equations with infinite delays

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

Caraballo Garrido, Tomás; Herrera Cobos, Marta; Marín Rubio, Pedro (Pergamon Press, 2015-01-01)
This paper is devoted to study the asymptotic behavior of a time-dependent parabolic equation with nonlocal diffusion and ...
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Chemostats with time-dependent inputs and wall growth

Caraballo Garrido, Tomás; Xiaoying, Han; Kloeden, Peter E. (Natural Sciences Publishing Corporation, 2015-01-01)
Traditional assumptions in the simple chemostat model include fixed availability of the nutrient and its supply rate, and ...
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Well--posedness and asymptotic behaviour for a non-classical and non-autonomous diffusion equation with delay

Caraballo Garrido, Tomás; Márquez Durán, Antonio Miguel; Rivero Garvía, Luis Felipe (2015-01-01)
In this paper, it is analyzed a non-classical non-autonomous di_usion equation with delay. First, the well-posedness and ...
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Nonautonomous chemostats with variable delays

Caraballo Garrido, Tomás; Xiaoying, Han; Kloeden, Peter E. (Society for Industrial and Applied Mathematics, 2015-01-01)
The appearance of delay terms in a chemostat model can be fully justified since the future behavior of a dynamical system ...
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Morse decomposition of global attractors with infinite components

Caraballo Garrido, Tomás; Jara Pérez, Juan Carlos; Langa Rosado, José Antonio; Valero Cuadra, José (2015-01-01)
In this paper we describe some dynamical properties of a Morse decomposition with a countable number of sets. In particular, ...
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Attractors for non-autonomous retarded lattice dynamical systems

Caraballo Garrido, Tomás; Morillas Jurado, Francisco; Valero Cuadra, José (De Gruyter Open, 2015-01-01)
In this paperwe study a non-autonomous lattice dynamical system with delay. Under rather general growth and dissipative ...
PhD Thesis
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Caracterización de los atractores en sistemas dinámicos no autónomos

Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Jara Pérez, Juan Carlos (2014-03-21)
El estudio de los sistemas dinámicos es de gran importancia, ya que están relacionados con fenómenos del mundo real. Los ...
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Stability of stationary solutions to 2D-Navier-Stokes models with delays

Caraballo Garrido, Tomás; Xiaoying, Han (International Press, 2014-01-01)
In this paper we establish some sufficient conditions for the exponential stability of the stationary solution to a ...
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Asymptotic Behaviour of a Logistic Lattice System

Caraballo Garrido, Tomás; Morillas Jurado, Francisco; Valero Cuadra, José (2014-01-01)
In this paper we study the asymptotic behaviour of solutions of a lattice dynamical system of a logistic type. Namely, we ...
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Asymptotic behavior of neutral stochastic partial functional integro-differential equations driven by a fractional Brownian motion

Caraballo Garrido, Tomás; Diop, Mamadou Abdoul; Ndiaye, Abdoul Aziz (2014-01-01)
This paper deals with the existence, uniqueness and asymptotic behavior of mild solutions to neutral stochastic delay ...
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Asymptotic Behaviour of a Non-Autonomous Lorenz-84 System

Anguiano Moreno, María; Caraballo Garrido, Tomás (2014-01-01)
The so called Lorenz-84 model has been used in climatological studies, for example by coupling it with a low-dimensional ...
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Stability of delay evolution equations with stochastic perturbations

Caraballo Garrido, Tomás; Shaikhet, Leonid (2014-01-01)
The investigation of stability for hereditary systems is often related to the construction of Lyapunov functionals. The ...
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On Differential Equations with Delay in Banach Spaces and Attractors for Retarded Lattice Dynamical Systems

Caraballo Garrido, Tomás; Morillas Jurado, Francisco; Valero Cuadra, José (2014-01-01)
In this paper we first prove a rather general theorem about existence of solutions for an abstract differential equation ...
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Pullback attractor for a non-linear evolution equation in elasticity

Caraballo Garrido, Tomás; Colucci, Renato (2014-01-01)
We prove the existence of a pullback attractor for a non{autonomous fourth order evolution equation arising in the fi eld ...
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Practical asymptotic stability of nonlinear stochastic evolution equations

Caraballo Garrido, Tomás; Hammami, Mohamed Ali; Mchiri, Lassaad (2014-01-01)
In this paper we establish some su cient conditions ensuring almost sure practical asymptotic stability with a non-exponential decay rate for solutions to stochastic evolution equations based on Lyapunov techniques.
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Fixed points and exponential stability for stochastic partial integro–differential equations with delays

Caraballo Garrido, Tomás; Diop, Mamadou Abdoul; Ndoye, Ahmet Seyni (Research India Publications, 2014-01-01)
In this paper, we study the existence and asymptotic stability in the pth-moment of mild solutions of nonlinear impulsive ...
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Existence results fortime-dependent neutral functional integrodifferential equations driven by a fractional Brownian motion

Caraballo Garrido, Tomás; Diop, Mamadou Abdoul; Ndiaye, Abdoul Aziz (Euclidean Press, 2014-01-01)
This article presents some results on existence and uniqueness of mild solutions to neutral stochastic functional evolution ...
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Pullback attractors for a non-autonomous integro-differential equation with memory in some unbounded domains

Anguiano Moreno, María; Caraballo Garrido, Tomás; Real Anguas, José (2013-01-01)
The main aim of this paper is to analyse the asymptotic behaviour of a non-autonomous integrodifferential parabolic equation ...
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Non-autonomous morse-decomposition and Lyapunov functions for gradient-like processes

Aragão Costa, Eder Ritis; Caraballo Garrido, Tomás; Carvalho, Alexandre Nolasco; Langa Rosado, José Antonio (2013-01-01)
We define (time dependent) Morse-decompositions for non-autonomous evolution processes (non-autonomous dynamical systems) ...
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Pullback attractors for differential equations with multiple variable delays in Lipschitz nonlinearities

Caraballo Garrido, Tomás; Kiss, Gábor; Taniguchi, Takeshi (2013-01-01)
We establish the results on the existence of pullback attractors for nonautonomous functional differential equations with ...
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Neutral stochastic delay partial functional integro-differential equations driven by a fractional Brownian motion

Caraballo Garrido, Tomás; Diop, Mamadou Abdoul (2013-01-01)
This paper deals with the existence and uniqueness of mild solutions to neutral stochastic delay functional integro-di ...
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On the Structure of the Global Attractor for Infinite-Dimensional Non-Autonomous Dynamical Systems with Weak Convergence

Caraballo Garrido, Tomás; Cheban, David (2013-01-01)
The aim of this paper is to describe the structure of global attractors for infinite-dimensional non-autonomous dynamical ...
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The three dimensional globally modified Navier-Stokes equations: Recent developments

Caraballo Garrido, Tomás; Kloeden, Peter E. (2013-01-01)
The globally modified Navier-Stokes equations (GMNSE) were introduced by Caraballo, Kloeden & Real in 2006 and have been ...
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Attractivity for Neutral Functional Differential Equations

Caraballo Garrido, Tomás; Kiss, Gábor (2013-01-01)
We study the long term dynamics of non-autonomous functional di fferential equations. Namely, we establish existence results ...
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Existence, uniqueness and asymptotic behavior of solutions for a nonclassical diffusion equation with delay

Caraballo Garrido, Tomás; Márquez Durán, Antonio Miguel (2013-01-01)
A nonclassical nonautonomous diffusion equation with delay is analyzed. First, we prove the existence and uniqueness of ...
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Random attractors for stochastic 2D-Navier-Stokes equations in some unbounded domains

Brzezniak, Zdzislaw; Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Li, Yuhong; Lukaszewicz, Grzegorz; Real Anguas, José (2013-01-01)
We show that the stochastic flow generated by the 2-dimensional Stochastic Navier-Stokes equations with rough noise on a ...
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Skew Product Semiflows and Morse Decomposition

Bortolan, Matheus Cheque; Caraballo Garrido, Tomás; Carvalho, Alexandre Nolasco; Langa Rosado, José Antonio (2013-01-01)
This paper is devoted to the investigation of the dynamics of non-autonomous differential equations. The description of ...
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An Estimate On the Fractal Dimension of Attractors of Gradient-Like Dynamical Systems

Bortolan, Matheus Cheque; Caraballo Garrido, Tomás; Carvalho, Alexandre Nolasco; Langa Rosado, José Antonio (2012-01-01)
This paper is dedicated to estimate the fractal dimension of exponential global attractors of some generalized gradient-like ...
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Continuity of Lyapunov Functions and of Energy Level for a Generalized Gradient Semigroup

Aragão Costa, Eder Ritis; Caraballo Garrido, Tomás; Carvalho, Alexandre Nolasco; Langa Rosado, José Antonio (2012-01-01)
The global attractor of a gradient-like semigroup has a Morse decomposition. Associated to this Morse decomposition there ...
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Gradient Infinite-Dimensional Random Dynamical Systems

Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Liu, Zenxhin (2012-01-01)
In this paper we introduce the concept of a gradient random dynamical system as a random semiflow possessing a continuous ...
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Random attractors for stochastic lattice systems with non-Lipschitz non-linearity

Caraballo Garrido, Tomás; Morillas Jurado, Francisco; Valero Cuadra, José (2012-01-01)
In this paper we study the asymptotic behaviour of solutions of a first-order stochastic lattice dynamical system with an ...
PhD Thesis
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Atractores para EDP parabólicas no lineales y no autónomas en dominios no acotados

Caraballo Garrido, Tomás; Real Anguas, José; Valero Cuadra, José; Anguiano Moreno, María (2011-09-01)
Este trabajo está dividido en cinco capítulos. En los Capítulos 1 y 3, se trata la parte teórica de los sistemas dinámicos ...
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A Non-Autonomous Strongly Damped Wave Equation: Existence and Continuity of the Pullback Attractor

Caraballo Garrido, Tomás; Carvalho, Alexandre Nolasco; Langa Rosado, José Antonio; Rivero Garvía, Luis Felipe (2011-01-01)
In this paper we consider the strongly damped wave equation with time dependent terms utt − u − γ(t) ut + β"(t)ut = f(u), ...
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Almost Periodic and Asymptotically Almost Periodic Solutions of Liénard Equations

Caraballo Garrido, Tomás; Cheban, David (2011-01-01)
The aim of this paper is to study the almost periodic and asymptotically almost periodic solutions on (0,+1) of the Li´enard ...
PhD Thesis
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Atractores pullback existencia y estructura para una ecuación de ondas con amortiguamiento no autónomo

Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Rivero Garvía, Luis Felipe (2011-01-01)
Este trabajo está dividido en dos partes. Una primera en la que se trata la parte teórica de los sistemas dinámicos autónomos ...
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The existence and exponential behavior of solutions to stochastic delay evolution equations with a fractional brownian motion

Caraballo Garrido, Tomás; Garrido Atienza, María José; Taniguchi, Takeshi (2011-01-01)
In this paper we investigate the existence, uniqueness and exponential asymptotic behavior of mild solutions to stochastic ...
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Stability of Gradient Semigroups Under Perturbations

Aragão Costa, Eder Ritis; Caraballo Garrido, Tomás; Carvalho, Alexandre Nolasco; Langa Rosado, José Antonio (2011-01-01)
In this paper we prove that gradient-like semigroups (in the sense of Carvalho and Langa (2009 J. Diff. Eqns 246 2646–68)) ...
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On the asymptotic behaviour of a stochastic 3D Lans-Alpha model

Caraballo Garrido, Tomás; Márquez Durán, Antonio Miguel; Real Anguas, José (2011-01-01)
The long-time behaviour of a stochastic 3D LANS-® model on a bounded domain is analysed. First, we reformulate the model ...
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Asymptotic behaviour of a stochastic semilinear dissipative functional equation without uniqueness of solutions

Caraballo Garrido, Tomás; Garrido Atienza, María José; Schmalfuss, Björn; Valero Cuadra, José (2010-01-01)
In this work we present the existence and uniqueness of pullback and random attractors for stochastic evolution equations ...
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Recent developments in dynamical systems: three perspectives

Balibrea Gallego, Francisco; Caraballo Garrido, Tomás; Kloeden, Peter E.; Valero Cuadra, José (2010-01-01)
This paper aims to an present account of some problems considered in the past years in Dynamical Systems, new research directions and also provide some open problems.
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Three-dimensional system of globally modified Navier-Stokes equations with delay

Caraballo Garrido, Tomás; Real Anguas, José; Márquez, Antonio M. (2010-01-01)
We prove the existence and uniqueness of strong solutions of a three-dimensional system of globally modified Navier–Stokes ...
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Existence of Pullback Attractors for Pullback Asymptotically Compact Processes

Caraballo Garrido, Tomás; Carvalho, Alexandre Nolasco; Langa Rosado, José Antonio; Rivero Garvía, Luis Felipe (2010-01-01)
This paper is concerned with the existence of pullback attractors for evolution processes. Our aim is to provide results ...
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Global attractor for a non-autonomous integro-differential equation in materials with memory

Caraballo Garrido, Tomás; Garrido Atienza, María José; Schmalfuss, Björn; Valero Cuadra, José (2010-01-01)
The long-time behavior of an integro-differential parabolic equation of diffusion type with memory terms, expressed by ...
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H2-boundedness of the pullback attractor for a non-nutonomous reaction-diffusion equation

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

Anguiano Moreno, María; Caraballo Garrido, Tomás; Real Anguas, José; Valero Cuadra, José (2010-01-01)
The existence of a pullback attractor for a reaction-diffusion equations in an unbounded domain containing a non-autonomous ...
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Almost periodic and almost automorphic solutions of linear differential equations

Caraballo Garrido, Tomás; Cheban, David (2010-01-01)
We analyze the existence of almost periodic (respectively, almost automorphic, recurrent) solutions of a linear non-homogeneous ...
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Almost periodic and almost automorphic solutions of linear differential/difference equations without Favard's separation condition. II

Caraballo Garrido, Tomás; Cheban, David (2009-01-01)
In this paper we continue the research started in a previous paper, where we proved that the linear differential equation (1) ...
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Almost periodic and almost automorphic solutions of linear differential/difference equations without Favard's separation condition. I

Caraballo Garrido, Tomás; Cheban, David (2009-01-01)
The well-known Favard's theorem states that the linear differential equation x′=A(t)x+f(t) Turn MathJax on with Bohr ...
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A gradient-like non autonomous evolution process

Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Rivero Garvía, Luis Felipe; Carvalho, Alexandre Nolasco (2009-01-01)
In this paper we consider a dissipative damped wave equation with non-autonomous damping of the form utt + ¯(t)ut = ¢u + ...
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Asymptotic Behaviour of the Three-Dimensional Á-Navier-Stokes Model with Locally Lipschitz Delay Forcing Terms

Caraballo Garrido, Tomás; Márquez Durán, Antonio Miguel; Real Anguas, José (2009-01-01)
We obtain some results on the existence and uniqueness, and exponential stability of solutions for the three-dimensional ...
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Non-Autonomous Attractor for Integro-Differential Evolution Equations

Caraballo Garrido, Tomás; Kloeden, Peter E. (2009-01-01)
We show that infinite-dimensional integro-differential equations which involve an integral of the solution over the time ...
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Attractors for Differential Equations with Multiple Variable Delays

Caraballo Garrido, Tomás; Kiss, Gábor (2009-01-01)
We establish some results on the existence of pullback attractors for non-autonomous delay di fferential equations with ...
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Attractors for Stochastic Lattice Dynamical Systems with a Multiplicative Noise

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

Caraballo Garrido, Tomás; Kloeden, Peter E.; Real Anguas, José (2008-01-01)
We obtain regularity results for solutions of the three dimensional system of globally modified Navier-Stokes equations, ...
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Synchronization of Systems with Multiplicative Noise

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

Caraballo Garrido, Tomás; Chueshov, Igor D.; Real Anguas, José (2008-01-01)
We study the asymptotic behaviour of a non-autonomous stochastic reaction-diffusion equation with memory. In fact, we prove ...
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Stabilisation of differential inclusions and PDEs without uniqueness by noise

Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Valero Cuadra, José (2008-01-01)
We prove that the asymptotic behaviour of partial differential inclusions and partial differential equations without ...
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Non-autonomous and random attractors for delay random semilinear equations without uniqueness

Caraballo Garrido, Tomás; Garrido Atienza, María José; Schmalfuss, Björn; Valero Cuadra, José (2008-01-01)
We first prove the existence and uniqueness of pullback and random attractors for abstract multi-valued non-autonomous and ...
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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 (2007-09-01)
En primer lugar probamos la existencia y unicidad de atractor para sistemas dinámicos multivaluados abstractos, tanto en ...
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Numerical and finite delay approximations of attractors for logistic differential-integral equations with infinite delay

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

Caraballo Garrido, Tomás; Marín Rubio, Pedro; Valero Cuadra, José (Elsevier, 2007-01-01)
We prove the existence of attractors for some types of differential problems containing infinite delays. Applications and ...
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Levitan/Bohr Almost Periodic and Almost Automorphic Solutions of Second-Order Monotone Differential Equations

Caraballo Garrido, Tomás; Cheban, David (2007-01-01)
The aim of this paper is to prove the existence of Levitan/Bohr almost periodic, almost automorphic, recurrent and Poisson ...
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Method of Lyapunov Functionals Construction in Stability of Delay Evolution Equations

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

Caraballo Garrido, Tomás; Chueshov, Igor D.; Marín Rubio, Pedro; Real Anguas, José (2007-01-01)
The existence and uniqueness of solutions for a stochastic reaction-diffusion equation with infinite delay is proved. ...
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Synchronization of a Stochastic Reaction-Diffusion System On a Thin Two-Layer Domain

Caraballo Garrido, Tomás; Chueshov, Igor D.; Kloeden, Peter E. (2007-01-01)
A system of semilinear parabolic stochastic partial differential equations with additive space-time noise is considered ...
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The Exponential Stability of Neutral Stochastic Delay Partial Differential Equations

Caraballo Garrido, Tomás; Real Anguas, José; Taniguchi, Takeshi (2007-01-01)
In this paper we analyse the almost sure exponential stability and ultimate boundedness of the solutions to a class of ...
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Existence of exponentially attracting stationary solutions for delay evolution equations

Caraballo Garrido, Tomás; Garrido Atienza, María José; Schmalfuss, Björn (2007-01-01)
We consider the exponential stability of semilinear stochastic evolution equations with delays when zero is not a solution ...
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Recent results on stabilization of PDEs by noise

Caraballo Garrido, Tomás (Sociedad Española de Matemática Aplicada, 2006-12-01)
This paper is intended to be a brief review on some recent results on the stabilization effect produced by noise in phenomena ...
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Comparison of the long-time behaviour of linear Ito and Stratonovich partial differential equations

Caraballo Garrido, Tomás; Langa Rosado, José Antonio (2006-01-01)
In this paper, we point out the different long-time behaviour of stochastic partial differential equations when one considers ...
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On the existence and uniqueness of solutions to stochastic three-dimensional Lagrangian averaged Navier-Stokes equations

Caraballo Garrido, Tomás; Real Anguas, José; Taniguchi, Takeshi (2006-01-01)
We prove existence and uniqueness of solutions for a stochastic version of the 3DLagrangian averaged Navier-Stokes (LANS-®) ...
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Pullback and forward attractors for a 3D Lans-alpha model with delay

Caraballo Garrido, Tomás; Márquez Durán, Antonio Miguel; Real Anguas, José (2006-01-01)
We analyse the asymptotic behaviour of a 3D Lagrangian averaged Navier-Stokes -model (3D LANS) with delays. In fact, we ...
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Discretization of Asymptotically Stable Stationary Solutions of Delay Differential Equations with a Random Stationary Delay

Caraballo Garrido, Tomás; Kloeden, Peter E.; Real Anguas, José (2006-01-01)
We prove the existence of a stationary random solution to a delay random ordinary differential system which attracts all ...
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Global and Pullback Attractors of Set-Valued Skew Product Flows

Caraballo Garrido, Tomás; Kloeden, Peter E.; Marín Rubio, Pedro (2006-01-01)
We investigate the asymptotic behaviour of a general set-valued skew product flow (SVSPF), that is, a set-valued cocycle ...
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Pullback attractors for non-autonomous 2D-Navier-Stokes equations in some unbounded domains

Caraballo Garrido, Tomás; Lukaszewicz, Grzegorz; Real Anguas, José (2006-01-01)
In this Note we first introduce the concept of pullback asymptotic compactness. Next, we establish a result ensuring the ...
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Stability of Nonlinear Functional Stochastic Evolution Equations of Second Order in Time

Caraballo Garrido, Tomás; Garrido Atienza, María José; Real Anguas, José (2006-01-01)
Sufficient conditions for exponential mean square stability of solutions to delayed stochastic partial differential equations ...
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Stabilization of Stationary Solutions of Evolution Equations by Noise

Caraballo Garrido, Tomás; Kloeden, Peter E.; Schmalfuss, Björn (2006-01-01)
We investigate the existence, uniqueness and exponential stability of non-constant stationary solutions of stochastic ...
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The pathwise numerical approximation of stationary solutions of semilinear stochastic evolution equations

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

Caraballo Garrido, Tomás; Lukaszewicz, Grzegorz; Real Anguas, José (2006-01-01)
First, we introduce the concept of pullback asymptotically compact non-autonomous dynamical system as an extension of the ...
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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. (2006-01-01)
We investigate the effect of perturbing the Chafee-Infante scalar reaction diffusion equation, ut−Δu = βu−u3, by noise. ...
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Autonomous and non-autonomous attractors for differential equations with delays

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

Caraballo Garrido, Tomás; Real Anguas, José; Márquez Durán, Antonio Miguel (2005-01-01)
"Como es bien conocido, las ecuaciones de Navier-Stokes gobiernan el movimiento de fluidos comunes como el agua, el aire, ...
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Asymptotic Behaviour of Monotone Multi-Valued Dynamical Systems

Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Valero Cuadra, José (2005-01-01)
We introduce the concept of a monotone multi-valued semi- ow as an order-preserving map. This de nition is motivated by ...
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Addendum To "Global Attractors for Multivalued Randomnamical Systems'' [Nonlinear Analysis 48(2002) 805-829]

Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Valero Cuadra, José (2005-01-01)
The aim of this note is to clarify a misleading statement which appeared in our fi rst paper dealing with the concept of global random attractor for multivalued random dynamical systems, as well as in the subsequent work
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The persistence of synchronization under environmental noise

Caraballo Garrido, Tomás; Kloeden, Peter E. (2005-01-01)
It is shown that the synchronization of dissipative systems persists when they are disturbed by additive noise no matter ...
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Existence of invariant manifolds for coupled parabolic and hyperbolic stochastic partial differential equations

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

Caraballo Garrido, Tomás; Márquez Durán, Antonio Miguel; Real Anguas, José (2005-01-01)
Existence and uniqueness of solutions for a stochastic version of the 3D-Lagrangian averaged Navier-Stokes (LANS-®) equation in a bounded domain and containing some hereditary characteristics are proved.
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Attractors for 2D-Navier-Stokes models with delays

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

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

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

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

Real Anguas, José; Caraballo Garrido, Tomás; Marín Rubio, Pedro (2003-05-23)
La memoria está compuesta de dos partes: la primera se enmarca dentro del Análisis Estocástico y la segunda parte en la ...
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Pullback attractors of nonautonomous and stochastic multivalued dynamical systems

Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Melnik, Valery S.; Valero Cuadra, José (2003-01-01)
In this paper we study the existence of pullback global attractors for multivalued processes generated by differential ...
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On the relationship between solutions of stochastic and random differential inclusions

Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Valero Cuadra, José (2003-01-01)
Some results on the relationship of the solutions of a stochastic di erential inclusion and the corresponding random di ...
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Asymptotic stability of nonlinear stochastic evolution equations

Caraballo Garrido, Tomás; Garrido Atienza, María José; Real Anguas, José (2003-01-01)
Some results on the pathwise asymptotic stability of solutions to stochastic partial differential equations are proved. ...
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A Comparison Between Two Theories for Multi-Valued Semiflows and Their Asymptotic Behaviour

Caraballo Garrido, Tomás; Marín Rubio, Pedro; Robinson, James C. (2003-01-01)
This paper presents a comparison between two abstract frameworks in which one can treat multi-valued semiflows and their ...
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Asymptotic Behaviour of 2D-Navier-Stokes Equations with Delays

Caraballo Garrido, Tomás; Real Anguas, José (2003-01-01)
Some results on the asymptotic behaviour of solutions to Navier-Stokes equations when the external force contains some ...
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Weak pullback attractors of setvalued processes

Caraballo Garrido, Tomás; Kloeden, Peter E.; Marín Rubio, Pedro (2003-01-01)
Weak pullback attractors are de ned for nonautonomous setvalued processes and their existence and upper semi continuous ...
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Stochastic stabilization of differential systems with general decay rate

Caraballo Garrido, Tomás; Garrido Atienza, María José; Real Anguas, José (2003-01-01)
Some sufficient conditions concerning stability of solutions of stochastic differential evolution equations with general ...
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The dimension of attractors of nonautonomous partial differential equations

Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Valero Cuadra, José (2003-01-01)
The concept of nonautonomous (or cocycle) attractor has become a proper tool for the study of the asymptotic behaviour of ...
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The exponential behaviour of nonlinear stochastic functional equations of second order in time

Caraballo Garrido, Tomás; Garrido Atienza, María José; Real Anguas, José (2003-01-01)
Sufficient conditions for exponential mean square stability of solutions to delayed stochastic partial differential equations ...
PhD Thesis
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Algunos resultados de existencia, unicidad y estabilidad para EDP funcionales estocásticas no lineales

Caraballo Garrido, Tomás; Real Anguas, José; Garrido Atienza, María José (2002-01-01)
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Existence and uniqueness of solutions for delay stochastic evolution equations

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

Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Valero Cuadra, José (2002-01-01)
We introduce the concept of multivalued random dynamical system (MRDS) as a measurable multivalued flow satisfying the ...
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The Exponential Behaviour and Stabilizability of Stochastic 2D-Navier-Stokes Equations

Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Taniguchi, Takeshi (2002-01-01)
Some results on the pathwise exponential stability of the weak solutions to a stochastic 2D-Navier-Stokes equation are ...
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Attractors for differential equations with variable delays

Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Robinson, James C. (2001-01-01)
Using the relatively new concept of a pullback attractor, we present some results on the existence of attractors for differential equations with variable delay. We give a variety of examples to which our result applies.
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On the decay rate of solutions of non-autonomous differential systems

Caraballo Garrido, Tomás (2001-01-01)
Some results on the asymptotic behaviour of solutions of diff erential equations concerning general decay rate are proved. ...
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Approximation of attractors for multivalued random dynamical systems

Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Valero Cuadra, José (Masaryk University, 2001-01-01)
The concept of global attractor for stochastic partial differential inclusions has been recently introduced as a joint ...
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Asymptotic exponential stability for diffusion processes driven by stochastic differential equations in duals of nuclear spaces

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

Anguiano Moreno, María; Caraballo Garrido, Tomás; Real Anguas, José (2001-01-01)
Some exponential growth results for the pullback attractor of a reaction-diffusion when time goes to ¡1 are proved in this ...
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A Stochastic Pitchfork Bifurcation in a Reaction-Diffusion Equation

Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Robinson, James C. (2001-01-01)
We study in some detail the structure of the random attractor for the Chafee{Infante reaction{di¬usion equation perturbed ...
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Navier-Stokes Equations with Delays

Caraballo Garrido, Tomás; Real Anguas, José (2001-01-01)
Some results on the existence and uniqueness of solutions to Navier-Stokes equations when the external force contains some hereditary characteristics are proved.
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Nonlinear Partial Functional Differential Equations: Existence and Stability

Caraballo Garrido, Tomás (2001-01-01)
Existence and uniqueness of solutions for a class of nonlinear functional differential equations in Hilbert spaces are ...
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On Stabilization of Partial Differential Equations by Noise

Caraballo Garrido, Tomás; Liu, Kai; Mao, Xuerong (2001-01-01)
Some results on stabilization of (deterministic and stochastic) partial differential equations are established. In particular, ...
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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 (2001-01-01)
In this paper we consider a stochastic differential inclusion with multiplicative noise. It is shown that it generates a multivalued random dynamical system for which there also exists a global random attractor.
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Global attractors for multivalued random semiflows generated by random differential inclusions with additive noise

Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Valero Cuadra, José (2001-01-01)
We introduce the concept of multivalued random dynamical system (MRDS) as a measurable multivalued flow satisfying the ...
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Stochastic Functional Partial Differential Equations: Existence, Uniqueness and Asymptotic Decay Property

Caraballo Garrido, Tomás; Liu, Kai (2000-01-01)
Existence and uniqueness of strong solutions for a class of stochastic functional di fferential equations in Hilbert spaces ...
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Stability and random attractors for a reaction-diffusion equation with multiplicative noise

Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Robinson, James C. (2000-01-01)
We study the asymptotic behaviour of a reaction-diffusion equation, and prove that the addition of multiplicative white ...
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Tracking Properties of Trajectories On Random Attracting Sets

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

Caraballo Garrido, Tomás; Liu, Kai (1999-01-01)
A semilinear stochastic partial differential equation with variable delays is considered. Sufficient conditions for the ...
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On Exponential Stability Criteria of Stochastic Partial Differential Equations

Caraballo Garrido, Tomás; Liu, Kai (1999-01-01)
Some criteria for the mean square and almost sure exponential stability of nonlinear stochastic partial differential ...
PhD Thesis
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Atractores y comportamiento finito-dimensional en sistemas dinámicos aleatorios

Caraballo Garrido, Tomás; Langa Rosado, José Antonio (1998-01-01)
"En el Capítulo 1, presentamos una síntesis de los resultados básicos sobre atractores globales que pueden encontrarse en ...
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Upper Semicontinuity of Attractors for Small Random Perturbations of Dynamical Systems

Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Robinson, James C. (1998-01-01)
The relationship between random attractors and global attractors for dynamical systems is studied. If a partial differential ...
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On the Pathwise Exponential Stability of Nonlinear Stochastic Partial-Differential Equations

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

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

Caraballo Garrido, Tomás (1991-01-01)
We state some results on existence and uniqueness for the solution of non linear stochastic PDEs with deviating arguments. ...
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Non-Linear Stochastic Partial Differential Equations with Delays: Existence and Uniqueness of Solutions

Caraballo Garrido, Tomás (1991-01-01)
The main aim of this paper is to study stochastic PDE's with delay terms. In fact, we prove existence and uniqueness of ...
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Asymptotic Exponential Stability of Stochastic Partial Differential Equations with Delay

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

Caraballo Garrido, Tomás (Universidad de Extremadura, 1989-01-01)
PhD Thesis
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Algunos resultados de estabilidad de ecuaciones en derivadas parciales estocásticas con retardos

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

Caraballo Garrido, Tomás (1988-01-01)
Sufficient conditions for pathwise exponential stability of the zero solution of stochastic PDE with deviating argument ...