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Microlocal defect measures for a degenerate thermoelasticity system

Part of: Partial differential equations

Published online by Cambridge University Press:  17 April 2013

Amel Atallah-Baraket  and
Clotilde Fermanian Kammerer
Amel Atallah-Baraket
Affiliation:
Dpt. de Mathématiques, Faculté des Sciences de Tunis, Université de Tunis El Manar, 1060, Tunis, Tunisie ([email protected])
Clotilde Fermanian Kammerer
Affiliation:
LAMA UMR CNRS 8050, Université Paris Est - Créteil, 61, avenue du Général de Gaulle, 94010 Créteil Cedex, France ([email protected])
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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.

Keywords

thermoelasticity equations; energy density; microlocal defect measures

MSC classification

Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 13 , Issue 1 , January 2014 , pp. 145 - 181
Copyright
©Cambridge University Press 2013 

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