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

TL;DR

This paper investigates the stability of pullback attractors in a nonlocal reaction-diffusion system when parameters vary, demonstrating upper semicontinuous convergence under broad conditions in a non-autonomous setting.

Contribution

It extends previous results by proving the robustness of pullback attractors with respect to parameter changes in a fully non-autonomous framework.

Findings

Established upper semicontinuous convergence of attractors

Extended robustness results to more general nonlocal reaction-diffusion models

Applied the framework of tempered universes for non-autonomous analysis

Abstract

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.