An exponential growth condition in H2H2 for the pullback attractor of a non-autonomous reaction–diffusion equation

Some exponential growth results for the pullback attractor of a reaction–diffusion equation when time goes to −∞−∞ are proved in this paper. First, a general result about Lp∩H01 exponential growth is established. Then, under additional assumptions, an exponential growth condition in H2H2 for the pullback attractor of the non-autonomous reaction–diffusion equation is also deduced.