Pullback attractors for the norm-to-weak continuous process and application to the nonautonomous reaction–diffusion equations

摘要

In this paper, we introduce the concept of norm-to-weak continuous process in a Banach space, and obtain the existence of pullback attractors for this kind of process. Then we give a new method for proving the existence of the pullback attractors. As an application, we obtain the existence of pullback attractors for nonautonomous reaction–diffusion equation in H01 with exponential growth of the external force.