Attractors for a class of delayed reaction-diffusion equations with dynamic boundary conditions

Abstract

In this paper we study the asymptotic behavior of solutions for a class of nonautonomous reaction-diffusion equations with dynamic boundary conditions possessing finite delay. Under the polynomial conditions of reaction term, suitable conditions of delay terms and a minimal conditions of time-dependent force functions, we first prove the existence and uniqueness of solutions by using the Galerkin method. Then, we ensure the existence of pullback attractors for the associated process to the problem by proving some uniform estimates and asymptotic compactness properties (via an energy method). With an additional condition of time-dependent force functions, we prove that the boundedness of pullback attractors in smoother spaces.