On pullback attractors in H_0~1 for nonautonomous reaction-diffusion equations

摘要

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 reactiondiffusion system in H_0~1 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.