Stabilization of the wave equation with moving boundary

Abstract

We deal with the wave equation with assigned moving boundary ($0<x<a(t)$) upon which Dirichlet-Neuman boundary conditions are satisfied, here $a(t)$ is assumed to move slower than the light and periodically. We give a feedback which guarantees the exponential decay of the energy. The proof relies on a reduction theorem of Yoccoz. At the end we give a remark on the moving-pointwise stabilization problem.