On the stabilization of the elasticity system by the boundary

Article type: Research Article

Authors: Khenissi, Moez | Vodev, Georgi

Affiliations: Département de Mathématiques, Faculté des Sciences de Monastir, Tunisie. E-mail: moez.khenissi@fsg.rnu.tn | Université de Nantes, Département de Mathématiques, UMR 6629 du CNRS, 2, rue de la Houssinière, BP 92208, 44332 Nantes Cedex 03, France. E-mail: georgi.vodev@math.univ-nantes.fr

Abstract: We obtain free of resonances regions for the elasticity system in the exterior of a strictly convex body in R3 with dissipative boundary conditions under some natural assumptions on the behaviour of the geodesics on the boundary. To do so, we use the properties of the parametrix of the Neumann operator constructed in Duke Math. J. 78 (1995), 677–714. As a consequence, we obtain time decay estimates for the local energy of the solutions of the corresponding mixed boundary value problems.

Keywords: boundary stabilization, exterior domain, local energy decay, Rayleigh resonances

DOI: 10.3233/ASY-2008-0869

Journal: Asymptotic Analysis, vol. 58, no. 1-2, pp. 1-16, 2008