Pullback attractors of nonautonomous reaction–diffusion equations

Abstract

In this paper, firstly we introduce the concept of norm-to-weak continuous cocycle in Banach space and give a technical method to verify this kind of continuity, then we obtain some abstract results for the existence of pullback attractors about this kind of cocycle, using the measure of noncompactness. As an application, we prove the existence of pullback attractors in H 0 1 of the cocycle associated with the solutions for some nonlinear nonautonomous reaction–diffusion equations. The attractor pullback attracts all bounded subsets of H 0 1 in the norm of H 0 1 .