Existence of time-dependent attractor of wave equation in locally uniform space

Abstract

In this article, we study non-autonomous dynamical behavior of weakly damped wave equation in unbounded domain. First of all, we introduce the time-dependent locally uniform space. After that, the pullback asymptotical compactness is proved by applying the contractive function method. Eventually, we obtain the existence of ( H lu 1 ( R 3 ) × L lu 2 ( R 3 ) , H ρ 1 ( R 3 ) × L ρ 1 ( R 3 ) ) -time-dependent attractor of wave equation.