An exponential growth condition in H^2 for the pullback attractor of a non-autonomous reaction-diffusion equation

Abstract

Some exponential growth results for the pullback attractor of a reaction-diffusion when time goes to ¡1 are proved in this paper. First, a general result about Lp\H1 0 exponential growth is established. Then, under additional assumptions, an exponential growth condition in H2 for the pullback attractor of the non-autonomous reaction-diffusion equation is also deduced.