ON PULLBACK ATTRACTORS IN $H^1_0$ FOR NONAUTONOMOUS REACTION–DIFFUSION EQUATIONS

Abstract

Using a recent method based on the concept of the Kuratowski measure of noncompactness of a bounded set together with some new estimates of solutions, we prove the existence of a unique minimal pullback attractor for the evolutionary process associated with a nonautonomous nonlinear reaction–diffusion system in [Formula: see text] in which the right-hand side satisfies only a certain integrability condition. In particular, we generalize a result obtained recently in [Li & Zhong, 2007] where at most an exponential growth of the right-hand side has been assumed for times going to both plus and minus infinity.