Pullback attractors for a class of non-autonomous nonclassical diffusion equations

Abstract

We consider the first initial boundary value problem for the non-autonomous nonclassical diffusion equation ut-εΔu t-Δu+f(u)=g(t), ε∈[0,1], in a bounded domain in ℝn. Under a Sobolev growth rate of the nonlinearity f and a suitable exponential growth of the external force g, using the asymptotic a priori estimate method, we prove the existence of pullback D-attractors si;̂ in the space H01(Ω) and the upper semicontinuity of Aε̂ at ε=0. © 2010 Elsevier Ltd. All rights reserved.