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Pedro Marín-Rubio

Publications and source records attributed to Pedro Marín-Rubio.

6 recordsLinked to original sources
arXiv2026

On the robustness of pullback attractors for a nonlocal reaction-diffusion equation under perturbation

A parametric family of reaction-diffusion equations with nonlocal viscosity is considered. Existence of solutions and actually of pullback attractors is known from previous works. In this paper we obtain a robustness result of the attractors toward the corresponding minimal pullback attractor of the limiting problem. This result extends the ones obtained in \cite{5}. Actually here all terms (reactions, external forces and nonlocal viscosity functions) may vary with the parameter. The upper semicontinuous convergence of attractors is obtained under rather general assumptions and in a fully non-autonomous context using the framework of tempered universes.

math.AP↗
arXiv2026

Existence and characterization of attractors for a nonlocal reaction-diffusion equation having an energy functional

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 and strong solutions. Second, we obtain the existence of global attractors in both situations under rather weak assumptions by the defining a multivalued semiflow (which is a semigroup in the particular situation when uniqueness of the Cauchy problem is satisfied). Third, we characterize the attractor either as the unstable manifold of the set of stationary points or as the stable one when we consider solutions only in the set of bounded complete trajectories.

math.DS↗
arXiv2026

About the structure of attractors for a nonlocal Chafee-Infante problem

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 uniqueness of the Cauchy problem. First, we analyse the existence and properties of stationary points, showing that the problem undergoes the same cascade of bifurcations as in the Chafee-Infante equation. Second, we study the stability of the fixed points and establish that the semiflow is dynamically gradient. We prove that the attractor consists of the stationary points and their heteroclinic connections and analyse some of the possible connections.

math.DS↗
arXiv2025

Robustness of dynamically gradient multivalued dynamical systems

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 approximating a differential inclusion studied in [3], proving that the weak solutions of these problems generate a dynamically gradient multivalued semiflow with respect to suitable Morse sets.

math.AP↗
arXiv2024

Weak global attractor for the $3D$-Navier-Stokes equations via the globally modified Navier-Stokes equations

In this paper we obtain the existence of a weak global attractor for the three-dimensional Navier-Stokes equations, that is, a weakly compact set with an invariance property, that uniformly attracts solutions, with respect to the weak topology, for initial data in bounded sets. To that end, we define this weak global attractor in terms of limits of solutions of the globally modified Navier-Stokes equations in the weak topology. We use the theory of semilinear parabolic equations and $ε$-regularity to obtain the local well posedness for the globally modified Navier-Stokes equations and the existence of a global attractor and its regularity.

math.AP↗