Non-autonomous reaction-diffusion model with dynamic boundary conditions

We investigate the dynamics of a non-autonomous reaction diffusion model with dynamic boundary conditions. We first show that, under the same assumptions, the known L-2(Omega) x L-2(Omega) pullback D-attractor indeed can attract in L2+delta (Omega) x L2+delta (partial derivative Omega)-norm for any delta is an element of[0, infinity); then we prove the continuity of the solution in H-1(Omega) x H-1/2(partial derivative Omega) with respect to the initial data, and finally show that such attractor can also attract in H-1(Omega) x H-1/2 (partial derivative Omega)-norm under a slightly stronger integrability condition on the time-dependent external forcing term. The proofs are based on a new Nash-Moser-Alikakos type a priori estimate about the difference of solutions near the initial time. (C) 2016 Elsevier Inc. All rights reserved.