H2-boundedness of the pullback attractor for a non-nutonomous reaction-diffusion equation

摘要

We prove some regularity results for the pullback attractor of a reaction-diffusion model. First we establish a general result about H2-boundedness of invariant sets for an evolution process. Then, as a consequence, we deduce that the pullback attractor of a non-autonomous reaction-diffusion equation is bounded not only in L2 (­) H1 0 (­) but in H2 (­).