Upper semicontinuity of pullback attractors for nonclassical diffusion equations

Abstract

Our aim in this paper is to study the long time behavior, in terms of upper semicontinuous property of pullback attractors, of nonclassical diffusion equations with nonautonomous perturbation. Specifically, we prove that, under some proper assumptions, the pullback attractor {Aε(t)}t∊R of Eq. (1) and the global attractor A of Eq. (1) with ε=0 satisfy limε→0+ distX(Aε(t),A)=0 for any t∊R.