51 citations · 108 across the 23 of their papers we have counts for
24 papers
A Stochastic Model of Intracellular Calcium Concentrations
Tomás Caraballo, Macarena Gómez-Mármol, Ignacio Roldán
In this paper, we study a slow-fast model of Intracellular Calcium Concentrations (ICC) within a stochastic framework, where stochastic perturbations are introduced to capture the…
Asymptotic behavior of a semilinear problem in heat conduction with long time memory and non-local diffusion
Jiaohui Xu, Tomás Caraballo, José Valero
In this paper, the asymptotic behavior of a semilinear heat equation with long time memory and non-local diffusion is analyzed in the usual set-up for dynamical systems generated b…
Dynamics and numerical simulations to predict empirical antibiotic treatment of multi-resistant Pseudomonas aeruginosa infection
Javier López-de-la-Cruz, María Pérez-Aranda, Ana Alcudia +4
This work discloses an epidemiological mathematical model to predict an empirical treatment for dogs infected by Pseudomonas aeruginosa. This dangerous pathogen is one of the leadi…
A way to model stochastic perturbations in population dynamics models with bounded realizations
Tomás Caraballo, Renato Colucci, Javier López-de-la-Cruz +1
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 characteristic…
Convergence of solutions for a reaction-diffusion problem with fractional Laplacian
Jiaouhui Xu, Tomás Caraballo, José Valero
A kind of nonlocal reaction-diffusion equations on an unbounded domain containing fractional Laplacian operator is analyzed. To be precise, we prove the convergence of solutions of…
Exponential attractors with explicit fractal dimensions for retarded functional differential equations
Wenjie Hu, Tomás Caraballo
The aim of this paper is to propose a new method to construct exponential attractors for infinite dimensional dynamical systems in Banach spaces with explicit fractal dimension. Th…
Lyapunov exponents and invariant manifolds for stochastic linear partial functional differential equations
Wenjie Hu, Tomás Caraballo
The main purpose of this work is to characterize the almost sure local structure stability of solutions to a class of linear stochastic partial functional differential equations (S…
Topological dimensions of attractors for partial functional differential equations in Banach spaces
Wenjie Hu, Tomás Caraballo
The main objective of this paper is to obtain estimations of Hausdorff dimension as well as fractal dimension of global attractors and pullback attractors for both autonomous and n…
Topological dimensions of global attractors for a delayed reaction-diffusion equation on an unbounded domain
Wenjie Hu, Tomás Caraballo
The purpose of this paper is to investigate the existence and estimation of Hausdorff and fractal dimension of global attractors for a delayed reaction-diffusion equation on an unb…
Topological dimensions of random attractors for stochastic partial differential equations with delay
Wenjie Hu, Tomás Caraballo
The aim of this paper is to obtain an estimation of Hausdorff as well as fractal dimensions of random attractors for a class of stochastic partial differential equations with delay…
Random attractors for a stochastic nonlocal delayed reaction-diffusion equation on a semi-infinite interval
Wenjie Hu, Quanxin Zhu, Tomás Caraballo
The aim of this paper is to prove the existence and qualitative property of random attractors for a stochastic nonlocal delayed reaction-diffusion equation (SNDRDE) on a semi-infin…
Invariant manifolds for stochastic delayed partial differential equations of parabolic type
Wenjie Hu, Quanxin Zhu, Tomás Caraballo
The aim of this paper is to prove the existence and smoothness of stable and unstable invariant manifolds for a stochastic delayed partial differential equation of parabolic type.…
Long-time asymptotics of solutions and the modified pseudo-conformal conservation law for super-critical nonlinear Schrödinger equation
Vo Van Au, Tomas Caraballo, Nguyen Huy Tuan
In this paper, we discuss a class of nonlinear Schrödinger equations with the power-type nonlinearity: in $\mathbf R^N…
Asymptotic stability of evolution systems of probability measures for nonautonomous stochastic systems: Theoretical results and applications
Renhai Wang, Tomas Caraballo, Nguyen Huy Tuan
The limiting stability of invariant probability measures of time homogeneous transition semigroups for autonomous stochastic systems has been extensively discussed in the literatur…
Continuity and topological structural stability for nonautonomous random attractors
Tomás Caraballo, Alexandre N. Carvalho, José A. Langa +1
In this work, we study continuity and topological structural stability of attractors for nonautonomous random differential equations obtained by small bounded random perturbations…
On the initial value problem for a class of nonlinear biharmonic equation with time-fractional derivative
Anh Tuan Nguyen, Tomás Caraballo, Nguyen Huy Tuan
In this work, we investigate the IVP for a time-fractional fourth-order equation with nonlinear source terms. More specifically, we consider the time-fractional biharmonic with exp…
The effect of a small bounded noise on the hyperbolicity for autonomous semilinear differential equations
Tomás Caraballo, Alexandre N. de Carvalho, José A. Langa +1
In this work we study permanence of hyperbolicity for autonomous differential equations under nonautonomous random/stochastic perturbations. For the linear case, we study robustnes…
Pullback and uniform attractors for nonautonomous reaction-diffusion equation in Dumbbell domains
Maykel Belluzi, Tomás Caraballo, Marcelo J. D. Nascimento +1
This work is devoted to the study of the asymptotic behavior of nonautonomous reaction-diffusion equations in Dumbbell domains . Each $Ω_{\v…
Permanence of nonuniform nonautonomous hyperbolicity for infinite-dimensional differential equations
Tomás Caraballo, Alexandre N. Carvalho, José Antonio Langa +1
In this paper, we study stability properties of nonuniform hyperbolicity for evolution processes associated with differential equations in Banach spaces. We prove a robustness resu…
Existence and regularity results for terminal value problem for nonlinear fractional wave equations
Nguyen Huy Tuan, Tomás Caraballo, Tran Bao Ngoc +1
We consider the terminal value problem (or called final value problem, initial inverse problem, backward in time problem) of determining the initial value, in a general class of ti…
Corrigendum to the chapter "Some aspects concerning the dynamics of stochastic chemostats"
Tomás Caraballo, María J. Garrido-Atienza, Javier López-de-la-Cruz +1
In this paper we correct an error made in a previous work, where a misleading stochastic system was obtained due to a lapse concerning a sign in one of the equations at the beginni…
On the practical global uniform asymptotic stability of stochastic differential equations
Tomas Caraballo, Mohamed Ali Hammami, Lasaad Mchiri
The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, in particular, of stochastic differential systems. The m…
On the Structure of the Global Attractor for Non-autonomous Difference Equations with Weak Convergence
Tomás Caraballo, David Cheban
The aim of this paper is to describe the structure of global attractors for non-autonomous difference systems of equations with recurrent (in particular, almost periodic) coefficie…
Invariant manifolds for random and stochastic partial differential equations
Tomas Caraballo, Jinqiao Duan, Kening Lu +1
Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential…