Analysis of the Energy Decay of a Degenerated Thermoelasticity System

Details Analysis of the Energy Decay of a Degenerated Thermoelasticity System Analysis of the Energy Decay of a Degenerated Thermoelasticity System

2012-03-26

arxiv.org/abs/1203.5606v1

Mathematics

Analysis of PDEs

28 pages

Scientific paper

In this paper, we study a system of thermoelasticity with a degenerated 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 the one of a damped wave equation: propagation along the rays of 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 geometric optic.

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