Pullback Attractors for Non-autonomous Reaction-Diffusion Equations on R^n

TL;DR

This paper investigates the long-term behavior of solutions to non-autonomous reaction-diffusion equations on R^n, establishing the existence of pullback global attractors in L^2 and H^1 spaces despite unbounded external terms.

Contribution

It proves the existence of pullback global attractors for non-autonomous reaction-diffusion equations on R^n with unbounded external terms, using tail estimates and a priori bounds.

Findings

Existence of pullback global attractors in L^2(R^n) and H^1(R^n)

Solutions exhibit pullback asymptotic compactness

Method involves uniform tail estimates for solutions

Abstract

We study the long time behavior of solutions of the non-autonomous Reaction-Diffusion equation defined on the entire space R^n when external terms are unbounded in a phase space. The existence of a pullback global attractor for the equation is established in L^2(R^n) and H^1(R^n), respectively. The pullback asymptotic compactness of solutions is proved by using uniform a priori estimates on the tails of solutions outside bounded domains.