Homogenization and uniform stabilization of the wave equation in perforated domains (Q6584923)

In this paper, a nonlinear hyerbolic boundary-value problem in a perforated domain is considered, where the holes are assumed to be \(\varepsilon\)-periodically distributed, with identical and critical small capacity size, \(\varepsilon\) being the period. The existence and uniqueness of the micro-model are performed by the Faedo-Galerkin method. The homogenized model is obtained by the classical Cioranescu-Murat technique. Using microlocal analysis tools and under a geometric control condition, the stability result is obtained via a \(\varepsilon\)-uniform observability inequality for the corresponding energy, provided that the initial data are uniformly bounded.