Pullback attractors for a non-autonomous integro-differential equation with memory in some unbounded domains

Abstract

The main aim of this paper is to analyse the asymptotic behaviour of a non-autonomous integrodifferential parabolic equation of diffusion type with a memory term, expressed by convolution integrals involving infinite delays, in an unbounded domain. The assumptions imposed do not ensure uniqueness of solutions of the corresponding initial value problems. The theory of set-valued non-autonomous dynamical systems is applied to prove the existence of pullback attractors for our model. To do this, we first analyse an abstract version of the equation.