Attractor of a nonautonomous hyperbolic equation with a small parameter (Q1810267)

In a bounded domain \(\Omega\subset \mathbb{R}^n\), the author considers the equation \[ \varepsilon\partial^2_t u+\gamma(t)\partial_tu- \Delta u+f(u,t)+ \varphi(x,t)=0 \tag{1} \] with the Dirichlet boundary condition \(u |_{\partial \Omega}=0\). Here \(\varepsilon\in (0,\varepsilon_0]\) is a small parameter; the functions \(\gamma(t)\), \(f(u,t)\), \(\varphi(x,t)\) are translationally compact. The main goal is to study the long-time behaviour of (1) and to prove the existence of its uniform attractors. Moreover, he studies upper semicontinuity of the attractors at the point \(\varepsilon =0\).