Microlocal defect measures for a degenerate thermoelasticity system

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. A. Atallah-Baraket and C. Fermanian KammererSystem (1.1) has an energywhich decreases in time according to E(u, θ, t) − E(u, θ, 0) = −2 t 0 Ω