Time-dependent global attractors for the strongly damped wave equations with lower regular forcing term - Mei, Xinyu; Sun, Tao; Xie, Yongqin; Zhu, Kaixuan (Topological Methods in Nonlinear Analysis, 2022)
In this paper, based on a new theoretical framework oftime-dependent global attractors (Conti, Pata and Temam \cite{CPT13}),we consider the strongly damped wave equations $ε(t)u_{tt}-Δ u_{t}-Δ u+f(u)=g(x)$and establish the existence of attractorsin $\mathcal{H}_{t}=H_{0}^{1}(Ω)× L^{2}(Ω)$and $\mathcal{V}_{t}=H_{0}^{1}(Ω)× H_{0}^{1}(Ω)$, respectively.