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Browsing by Author "Caraballo Garrido, Tomás"
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A comparison between random and stochastic modeling for a SIR model [Article]
Caraballo Garrido, Tomás; Colucci, Renato (American Institute of Mathematical Sciences, 201701)In this article, a random and a stochastic version of a SIR nonautonomous model previously introduced in P. E. Kloeden and V. S. Kozyakin, The dynamics of epidemiological systems with nonautonomous and random coefficients, ...

A Comparison Between Two Theories for MultiValued Semiflows and Their Asymptotic Behaviour [Article]
Caraballo Garrido, Tomás; Marín Rubio, Pedro; Robinson, James C. (2003)This paper presents a comparison between two abstract frameworks in which one can treat multivalued semiflows and their asymptotic behaviour. We compare the theory developed by Ball [5] to treat equations whose solutions ...

A free boundary tumor model with time dependent nutritional supply [Article]
Sun, Wenlong; Caraballo Garrido, Tomás; Han, Xiaoying; Kloeden, Peter E. (Elsevier, 202006)A nonautonomous free boundary model for tumor growth is studied. The model consists of a nonlinear reaction diffusion equation describing the distribution of vital nutrients in the tumor and a nonlinear integrodifferential ...

A gradientlike non autonomous evolution process [Article]
Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Rivero Garvía, Luis Felipe; Carvalho, Alexandre Nolasco (2009)In this paper we consider a dissipative damped wave equation with nonautonomous damping of the form utt + ¯(t)ut = ¢u + f(u) (1) in a bounded smooth domain ½ Rn with Dirichlet boundary conditions, where f is a ...

A NonAutonomous Strongly Damped Wave Equation: Existence and Continuity of the Pullback Attractor [Article]
Caraballo Garrido, Tomás; Carvalho, Alexandre Nolasco; Langa Rosado, José Antonio; Rivero Garvía, Luis Felipe (2011)In this paper we consider the strongly damped wave equation with time dependent terms utt − u − γ(t) ut + β"(t)ut = f(u), in a bounded domain ⊂ Rn, under some restrictions on β"(t), γ(t) and growth restrictions on the ...

A qualitative description of microstructure formation and coarsening phenomena for an evolution equation [Article]
Caraballo Garrido, Tomás; Colucci, Renato (Springer, 201704)We provide a qualitative description of microstructure formation and coarsening phenomena for the solutions of a singularly perturbed fourth order evolution equation arising in the study of phase transitions. In particular ...

A random model for immune response to virus in fluctuating environments [Chapter of Book]
Asai, Yusuke; Caraballo Garrido, Tomás; Han, Xiaoying; Kloeden, Peter E. (Springer, 2016)In this work we study a model for virus dynamics with a random immune response and a random production rate of susceptible cells from cell proliferation. In traditional models for virus dynamics, the rate at which the ...

A Stochastic Pitchfork Bifurcation in a ReactionDiffusion Equation [Article]
Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Robinson, James C. (2001)We study in some detail the structure of the random attractor for the Chafee{Infante reaction{di¬usion equation perturbed by a multiplicative white noise, du = (¢u + u ¡ u3) dt + ¼ u ¯ dWt; x 2 D » Rm: First we prove, ...

A stochastic SIRI epidemic model with Lévy noise [Article]
Berrhazi, Badreddine; El Fatini, Mohamed; Caraballo Garrido, Tomás; Pettersson, Roger (American Institute of Mathematical Sciences, 2018)Some diseases such as herpes, bovine and human tuberculosis exhibit relapse in which the recovered individuals do not acquit permanent immunity but return to infectious class. Such diseases are modeled by SIRI models. In ...

A stochastic SIRI epidemic model with relapse and media coverage [Article]
Caraballo Garrido, Tomás; El Fatini, Mohamed; Pettersson, Roger; Taki, Regragui (American Institute of Mathematical Sciences, 2018)This work is devoted to investigate the existence and uniqueness of a global positive solution for a stochastic epidemic model with relapse and media coverage. We also study the dynamical properties of the solution around ...

A survey on impulsive dynamical systems [Presentation]
Bonotto, Everaldo de Mello; Bortolan, Matheus Cheque; Caraballo Garrido, Tomás; Collegari, Rodolfo (Bolyai Institute (University of Szeged), 2016)In this survey we provide an introduction to the theory of impulsive dynamical systems in both the autonomous and nonautonomous cases. In the former, we will show two different approaches which have been proposed to analyze ...

A survey on NavierStokes models with delays: Existence, uniqueness and asymptotic behavior of solutions [Article]
Caraballo Garrido, Tomás; Xiaoying, Han (2015)In this survey paper we review several aspects related to NavierStokes models when some hereditary characteristics (constant, distributed or variable delay, memory, etc) appear in the formulation. First some results ...

A way to model stochastic perturbations in population dynamics models with bounded realizations [Article]
Caraballo Garrido, Tomás; Colucci, Renato; López de la Cruz, Javier; Rapaport, Alain (Elsevier, 201910)In this paper, we analyze the use of the OrnsteinUhlenbeck process to model dynamical systems subjected to bounded noisy perturbations. In order to discuss the main characteristics of this new approach we consider some ...

Addendum To "Global Attractors for Multivalued Randomnamical Systems'' [Nonlinear Analysis 48(2002) 805829] [Article]
Caraballo Garrido, Tomás; Langa Rosado, José Antonio; Valero Cuadra, José (2005)The aim of this note is to clarify a misleading statement which appeared in our fi rst paper dealing with the concept of global random attractor for multivalued random dynamical systems, as well as in the subsequent work

Algunos resultados de estabilidad de ecuaciones en derivadas parciales estocásticas con retardos [PhD Thesis]
Caraballo Garrido, Tomás (1988)"En esta memoria presentamos una contribución al estudio de la estabilidad en la Ecuaciones en Derivadas Parciales Estocásticas (E.D.P.E) con retardo.Hemos estructurado nuestro trabajo en cuatro capítulos. En el primero ...

Algunos resultados de existencia, unicidad y estabilidad para EDP funcionales estocásticas no lineales [PhD Thesis]
Garrido Atienza, María José (2002) 
Almost periodic and almost automorphic solutions of linear differential equations [Article]
Caraballo Garrido, Tomás; Cheban, David (2010)We analyze the existence of almost periodic (respectively, almost automorphic, recurrent) solutions of a linear nonhomogeneous di erential (or di erence) equation in a Banach space, with almost periodic (respectively, ...

Almost periodic and almost automorphic solutions of linear differential/difference equations without Favard's separation condition. I [Article]
Caraballo Garrido, Tomás; Cheban, David (2009)The wellknown Favard's theorem states that the linear differential equation x′=A(t)x+f(t) Turn MathJax on with Bohr almost periodic coefficients admits at least one Bohr almost periodic solution if it has a bounded ...

Almost periodic and almost automorphic solutions of linear differential/difference equations without Favard's separation condition. II [Article]
Caraballo Garrido, Tomás; Cheban, David (2009)In this paper we continue the research started in a previous paper, where we proved that the linear differential equation (1) x0 = A(t)x + f(t) with Levitan almost periodic coefficients has a unique Levitan almost periodic ...

Almost Periodic and Asymptotically Almost Periodic Solutions of Liénard Equations [Article]
Caraballo Garrido, Tomás; Cheban, David (2011)The aim of this paper is to study the almost periodic and asymptotically almost periodic solutions on (0,+1) of the Li´enard equation x′′ + f(x)x′ + g(x) = F(t), where F : T ! R (T = R+ or R) is an almost periodic or ...