Upper semicontinuity of pullback attractors for a nonautonomous damped wave equation

Abstract

In this paper, we study the local uniformly upper semicontinuity of pullback attractors for a strongly damped wave equation. In particular, under some proper assumptions, we prove that the pullback attractor ${\{A_{\epsilon }(t)\}}_{t\in \mathbb{R}}$ of Eq. (1.1) with $\epsilon \in [0,1]$ satisfies ${lim}_{\epsilon \to {\epsilon }_0}{sup}_{t\in [a,b]}{dist}_{H_0^1\times L^2}(A_{\epsilon }(t),A_{{\epsilon }_0}(t))=0$ for any $[a,b]\subset \mathbb{R}$ and ${\epsilon }_0\in [0,1]$.