Exponential attractors for singularly perturbed damped wave equations: A simple construction

Abstract

This note is concerned with the damped wave equation ε²∂_ttu+∂_tu−Δu+f(u)=g depending on a small parameter ε and with the corresponding parabolic equation ∂_tu−Δu+f(u)=g obtained in the singular limit ε→0. The existence of a family ℳ_ε of exponential attractors which is Hölder continuous with respect to ε is proved.