Pullback attractors for non-autonomous reaction–diffusion equations with dynamical boundary conditions

Abstract

In this paper we prove the existence and uniqueness of a weak solution for a non-autonomous reaction–diffusion model with dynamical boundary conditions. After that, a continuous dependence result is established via an energy method, including in particular some compactness properties. Finally, the precedent results are used in order to ensure the existence of minimal pullback attractors in the frameworks of universes of fixed bounded sets and that given by a tempered growth condition. The relation among these families is also discussed.