Pullback dynamics of non-autonomous wave equations with acoustic boundary condition

Abstract

This paper is concerned with a class of wave equations with acoustic boundary condition subject to non-autonomous external forces. Under some general assumptions, the problem generates a well-posed evolution process. Then, we establish the existence of a minimal pullback attractor within a universe of tempered sets defined by the forcing terms. We also, study the upper semicontinuity of attractors as the non-autonomous perturbation tends to zero. Our results allow unbounded external forces and nonlinearities with critical growth.