On pullback attractors in H² for non-autonomous reaction-diffusion equations

摘要

In this paper we consider H2-regularity of pullback attractors for the reaction-diffusion equation. Firstly, we show that under the suitable conditions, every family of bounded subsets of L2(Ω) which is invariant for the process U, is in fact bounded in H2(Ω). Then, as a consequence, we obtain that the system has a unique continuous periodic solution which attracts any bounded set exponentially.