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Microlocal defect measures for a degenerate thermoelasticity system

Published online by Cambridge University Press:  17 April 2013

Amel Atallah-Baraket
Affiliation:
Dpt. de Mathématiques, Faculté des Sciences de Tunis, Université de Tunis El Manar, 1060, Tunis, Tunisie (amel.atallah@fst.rnu.tn)
Clotilde Fermanian Kammerer
Affiliation:
LAMA UMR CNRS 8050, Université Paris Est - Créteil, 61, avenue du Général de Gaulle, 94010 Créteil Cedex, France (Clotilde.Fermanian@u-pec.fr)

Abstract

In this paper, we study a system of thermoelasticity with a degenerate second-order operator in the heat equation. We analyze the evolution of the energy density of a family of solutions. We consider two cases: when the set of points where the ellipticity of the heat operator fails is included in a hypersurface and when it is an open set. In the first case, and under special assumptions, we prove that the evolution of the energy density is that of a damped wave equation: propagation along the rays of the geometric optic and damping according to a microlocal process. In the second case, we show that the energy density propagates along rays which are distortions of the rays of the geometric optic.

Type
Research Article
Copyright
©Cambridge University Press 2013 

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