Pullback attractors for a reaction-diffusion equation in a general nonempty open subset of R^N with non-autonomous forcing term in H^{−1}

Abstract

The existence of minimal pullback attractors in L^2(Ω) for a non-autonomous reaction-diffusion equation, in the frameworks of universes of fixed bounded sets and that given by a tempered growth condition, is proved in this paper, when the domain Ω is a general nonempty open subset of R^N, and h ∈ L^2_loc(R;H^{−1}(Ω)). The main concept used in the proof is the asymptotic com- pactness of the process generated by the problem. The relation among these families is also discussed.