Pullback attractors of non-autonomous nonclassical diffusion equations with state-dependent delay

Abstract

In this paper, we investigate the existence of pullback attractors for a non-autonomous nonclassical diffusion equation with state-dependent delay. First, the existence and uniqueness of strong solutions are proved via the standard Faedo-Galerkin method. To address the state-dependent delay, we incorporate its compensator into a normal functional, which enables us to obtain both the existence of a pullback absorbing set and the pullback asymptotic compactness of the corresponding evolution process. In particular, new properties of specific composition operators are derived to support the main results. Finally, we establish the existence of pullback attractors.