Homogenization and uniform stabilization of the wave equation in perforated domains

In this article we study the homogenization and uniform decay rates estimates of the energy associated to the damped nonlinear wave equation partial derivative(tt)u(epsilon) - Delta u(epsilon) + f (u(epsilon)) + a(x)g(partial derivative(t)u(epsilon)) = 0 in Omega(epsilon) x (0, infinity) where Omega(epsilon) is a domain containing holes with small capacity (i.e. the holes are smaller than a critical size). The homogenization's proofs are based on the abstract framework introduced by Cioranescu and Murat [14] for the study of homogenization of elliptic problems. The main goal of this article is to prove, in one shot, uniform decay rate estimates of the energy associated to solutions of the problem posed in the perforated domain Omega(epsilon) as well as for the limit case Omega when epsilon -> 0 by using refined arguments of microlocal analysis. (c) 2024 Elsevier Inc. All rights reserved.