Dirichlet boundary stabilization of the wave equation

Article type: Research Article

Authors: Ammari, Kais

Affiliations: Institut Élie Cartan, Département de Mathématiques, Université de Nancy I, F‐54506 Vandoeuvre‐lès‐Nancy cedex, France E‐mail: ammari@iecn.u‐nancy.fr

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.

Keywords: boundary stabilization, Dirichlet type boundary feedback, wave equation

Journal: Asymptotic Analysis, vol. 30, no. 2, pp. 117-130, 2002