Logarithmic stabilisation of a multidimensional structure by the boundary

Article type: Research Article

Authors: Ouksel, Leila

Affiliations: Université de Paris Sud, Mathématiques, Bât. 425, 91405 Orsay Cedex, France. E-mails: Leila.Ouksel@math.u-psud.fr, louksel@yahoo.fr

Abstract: We examine the decay of the energy for wave equations on a bounded domain Rn, connected through one point to a rod modelled by a segment of R. It is shown that the energy decreases at least as the inverse logarithm of time. This result is obtained using a dissipative condition of the Neumann type on the boundary of the domain.

Keywords: logarithmic stabilisation, wave equations, Carleman inequality, interpolation inequality

DOI: 10.3233/ASY-2012-1152

Journal: Asymptotic Analysis, vol. 80, no. 3-4, pp. 347-376, 2012