Uniform Gevrey regularity for the attractor of a damped wave equation (Q1422522)

The authors deal with the following singularly perturbed damped wave equation in a cube domain \(\Omega= [0,2\pi]^3\) \[ \begin{gathered} \varepsilon\partial^2_t u^\varepsilon+ \gamma\partial_t u^\varepsilon+ Au^\varepsilon+ f(u^\varepsilon)= g,\\ u^\varepsilon|_{t=0}= u_0,\quad \partial_t u^\varepsilon|_{t= 0}= u_1,\end{gathered} \] where the operator \(A\) is \(I-\Delta\) with periodic boundary conditions. Under suitable assumptions on \(f\), \(u_0\), \(u_1\), \(g\) the authors prove time-asymptotic regularity in Gevrey spaces and obtain the uniform bounds for the associated global and exponential attractors.