Dirichlet boundary stabilization of the wave equation

Abstract

We consider the stabilization problem for a wave equation. In the case when the geometric control assumption, see [3], is not satisfied, we prove that the energy of system decay with a logarithmic rate for all initial data in the domain of the infinitesimal generator of evolution equation. The technique used consists in deducing the decay estimate from an observability inequality for the associated undamped problem, via sharp regularity results.