H2H2-boundedness of the pullback attractor for a non-autonomous reaction–diffusion equation

We prove some regularity results for the pullback attractor of a reaction–diffusion model. First we establish a general result about H2H2-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(Ω)∩H01(Ω) but also in H2(Ω)H2(Ω).