Pullback attractors for nonautonomous wave equations with critical exponent

Abstract

In this paper, we prove the existence of a pullback attractor for a nonautonomous wave equation with critical exponent. To do this, we first use the concept of pullback D -asymptotic compactness given in [T. Caraballo, G. Łukaszewicz, J. Real, Pullback attractors for asymptotically compact nonautonomous dynamical systems, Nonlinear Anal. 64 (2006) 484–498] to show the existence of pullback attractor of nonautonomous dynamical systems, and then we give a new method for verifying the pullback D -asymptotic compactness.