Time-dependent global attractors for the strongly damped wave equations with lower regular forcing term

Abstract

In this paper, based on a new theoretical framework of time-dependent global attractors (Conti, Pata and Temam \cite{CPT13}), we consider the strongly damped wave equations $\varepsilon(t)u_{tt}-\Delta u_{t}-\Delta u+f(u)=g(x)$ and establish the existence of attractors in $\mathcal{H}_{t}=H_{0}^{1}(\Omega)\times L^{2}(\Omega)$ and $\mathcal{V}_{t}=H_{0}^{1}(\Omega)\times H_{0}^{1}(\Omega)$, respectively.