Browsing by Author "Caraballo Garrido, Tomás"
Now showing items 1-20 of 218
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A comparison between random and stochastic modeling for a SIR model [Article]
(American Institute of Mathematical Sciences, 2017-01)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, ...
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A Comparison Between Two Theories for Multi-Valued Semiflows and Their Asymptotic Behaviour [Article]
(2003)This paper presents a comparison between two abstract frameworks in which one can treat multi-valued semiflows and their asymptotic behaviour. We compare the theory developed by Ball [5] to treat equations whose solutions ...
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A free boundary tumor model with time dependent nutritional supply [Article]
(Elsevier, 2020-06)A non-autonomous 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 integro-differential ...
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A gradient-like non autonomous evolution process [Article]
(2009)In this paper we consider a dissipative damped wave equation with non-autonomous 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 ...
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A Non-Autonomous Strongly Damped Wave Equation: Existence and Continuity of the Pullback Attractor [Article]
(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 ...
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A qualitative description of microstructure formation and coarsening phenomena for an evolution equation [Article]
(Springer, 2017-04)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 ...
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A random model for immune response to virus in fluctuating environments [Chapter of Book]
(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 ...
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A Stochastic Pitchfork Bifurcation in a Reaction-Diffusion Equation [Article]
(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, ...
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A stochastic SIRI epidemic model with Lévy noise [Article]
(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 ...
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A stochastic SIRI epidemic model with relapse and media coverage [Article]
(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 ...
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A survey on impulsive dynamical systems [Presentation]
(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 ...
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A survey on Navier-Stokes models with delays: Existence, uniqueness and asymptotic behavior of solutions [Article]
(2015)In this survey paper we review several aspects related to Navier-Stokes models when some hereditary characteristics (constant, distributed or variable delay, memory, etc) appear in the formulation. First some results ...
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A way to model stochastic perturbations in population dynamics models with bounded realizations [Article]
(Elsevier, 2019-10)In this paper, we analyze the use of the Ornstein-Uhlenbeck process to model dynamical systems subjected to bounded noisy perturbations. In order to discuss the main characteristics of this new approach we consider some ...
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Addendum To "Global Attractors for Multivalued Randomnamical Systems'' [Nonlinear Analysis 48(2002) 805-829] [Article]
(2005)The aim of this note is to clarify a misleading statement which appeared in our fi rst paper dealing with the concept of global random attractor for multivalued random dynamical systems, as well as in the subsequent work
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Algunos resultados de estabilidad de ecuaciones en derivadas parciales estocásticas con retardos [PhD Thesis]
(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 ...
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Almost periodic and almost automorphic solutions of linear differential equations [Article]
(2010)We analyze the existence of almost periodic (respectively, almost automorphic, recurrent) solutions of a linear non-homogeneous di erential (or di erence) equation in a Banach space, with almost periodic (respectively, ...
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Almost periodic and almost automorphic solutions of linear differential/difference equations without Favard's separation condition. I [Article]
(2009)The well-known 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 ...
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Almost periodic and almost automorphic solutions of linear differential/difference equations without Favard's separation condition. II [Article]
(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 ...
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Almost Periodic and Asymptotically Almost Periodic Solutions of Liénard Equations [Article]
(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 ...