51 citations · 90 across the 16 of their papers we have counts for
18 papers
Weak mean random attractors for non-local random and stochastic reaction-diffusion equations
Rubén Caballero, Pedro Marín-Rubio, José Valero
In this paper, we prove the existence of weak pullback mean random attractors for a non-local stochastic reaction-diffusion equation with a nonlinear multiplicative noise. Also, we…
About the structure of attractors for a nonlocal Chafee-Infante problem
Rubén Caballero, Alexandre Nolasco Carvalho, Pedro Marín-Rubio +1
In this paper, we study the structure of the global attractor for the multivalued semiflow generated by a nonlocal reaction-diffusion equation in which we cannot guarantee uniquene…
Existence and characterization of attractors for a nonlocal reaction-diffusion equation having an energy functional
Rubén Caballero, Pedro Marín-Rubio, José Valero
In this paper we study a nonlocal reaction-diffusion equation in which the diffusion depends on the gradient of the solution. We prove first the existence and uniqueness of regular…
Robustness of dynamically gradient multivalued dynamical systems
Rubén Caballero, Alexandre N. Carvalho, Pedro Marín-Rubio +1
In this paper we study the robustness of dynamically gradient multivalued semiflows. As an application, we describe the dynamical properties of a family of Chafee-Infante problems…
Generalized TCP-RED dynamical model for Internet congestion control
José M. Amigó, Guillem Duran, Angel Giménez +2
Adaptive management of traffic congestion in the Internet is a complex problem that can gain useful insights from a dynamical approach. In this paper we propose and analyze a one-d…
Chain recurrence and structure of omega-limit sets of multivalued semiflows
Oleksiy V. Kapustyan, Pavlo O. Kasyanov, José Valero
We study properties of !-limit sets of multivalued semiflows like chain recurrence or the existence of cyclic chains. First, we prove that under certain conditions the omega-limit…
Attractors for weak and strong solutions of the three-dimensional Navier-Stokes equations with damping
Daniel Pardo, José Valero, Ángel Giménez
In this paper we obtain the existence of global attractors for the dynamical systems generated by weak solution of the three-dimensional Navier-Stokes equations with damping. We co…
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…
Existence of periodic solutions for a scalar differential equation modelling optical conveyor belts
Luis Carretero, José Valero
We study a one-dimensional ordinary differential equation modelling optical conveyor belts, showing in particular cases of physical interest that periodic solutions exist. Moreover…
Characterization of the attractor for nonautonomous reaction-diffusion equations with discontinuous nonlinearity
José Valero
In this paper, we study the asymptotic behavior of the solutions of a nonautonomous differential inclusion modeling a reaction-diffusion equation with a discontinuous nonlinearity.…
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…
Bifurcation and hyperbolicity for a nonlocal quasilinear parabolic problem
José M. Arrieta, Alexandre N. Carvalho, Estefani M. Moreira +1
In this article, we study a one-dimensional nonlocal quasilinear problem of the form , with Dirichlet boundary conditions on the interval $[0,π…
The existence of isolating blocks for multivalued semiflows
Estefani M. Moreira, José Valero
In this article, we show the existence of an isolating block, a special neighborhood of an isolated invariant set, for multivalued semiflows acting on metric spaces (not locally co…
Structure of the attractor for a non-local Chafee-Infante problem
Estefani M. Moreira, José Valero
In this article, we study the structure of the global attractor for a non-local one-dimensional quasilinear problem. The strong relation of our problem with a non-local version of…
Internet congestion control: from stochastic to dynamical models
José M. Amigó, Angel Giménez, Oscar Martínez-Bonastre +1
Since its inception, control of data congestion on the Internet has been based on stochastic models. One of the first such models was Random Early Detection. Later, this model was…
A non-autonomous scalar one-dimensional dissipative parabolic problem: The description of the dynamics
Rita de Cássia D. S. Broche, Alexandre N. Carvalho, José Valero
The purpose of this paper is to give a characterization of the structure of non-autonomous attractors of the problem when the parameter varies.…
Structure and regularity of the global attractor of a reaction-di§usion equation with non-smooth nonlinear term
Oleksiy V. Kapustyan, Pavlo O. Kasyanov, José Valero
In this paper we study the structure of the global attractor for a reaction- di§usion equation in which uniqueness of the Cauchy problem is not guarantied. We prove that the global…
A weak comparison principle for reaction-diffusion systems
José Valero
In this paper we prove a weak comparison principle for a reaction-diffusion system without uniqueness of solutions. We apply the abstract results to the Lotka-Volterra system with…