Solution and Asymptotic Behavior for a Nonlocal Coupled System of Reaction-Diffusion

TL;DR

This paper investigates the existence, uniqueness, and long-term behavior of solutions for a nonlocal coupled reaction-diffusion system, providing theoretical proofs and a numerical scheme.

Contribution

It improves previous results on coupled systems by establishing existence, uniqueness, and exponential decay of solutions with a new numerical approach.

Findings

Existence and uniqueness of weak solutions proven.

Solutions exhibit exponential decay over time.

A numerical scheme for the system is developed.

Abstract

This paper concerns with existence, uniqueness and asymptotic behavior of the solutions for a nonlocal coupled system of reaction-diffusion. We prove the existence and uniqueness of weak solutions by the Faedo-Galerkin method and exponential decay of solutions by the classic energy method. We improve the results obtained by Chipot-Lovato and Menezes for coupled systems. A numerical scheme is presented.