Title: Cauchy problem for linear thermoelastic systems, Part I: A unified approach

Authors: Kay Jachmann, Michael Reissig

Addresses: Am Berge 13, 18273 Gustrow, Germany. ' Faculty for Mathematics and Computer Science, TU Bergakademie Freiberg, Pruferstr. 9, 09596 Freiberg, Germany

Abstract: We present a unified approach for studying qualitative properties of solutions to Cauchy problems for several linear thermoelasticity models, i.e., the classical (or type-1), type-2, type-3 and second sound models (with possible lower order terms), for isotropic media. The main focus lies on the problems in one space dimension, but possible extensions to treat higher dimensional cases are discussed. The approach is based on a diagonalisation procedure, and the obtained solution representations will be used to derive results on well-posedness, L^p-L^q decay estimates, diffusion phenomena and on the propagation of singularities. The considerations of this paper are part of Jachmann (2008).

Keywords: thermoelasticity models; unified approach; hyperbolic-parabolic coupled diagonalisation; decay rates; diffusion phenomenon; singularities propagation; Cauchy problems.

DOI: 10.1504/IJDSDE.2009.031101

International Journal of Dynamical Systems and Differential Equations, 2009 Vol.2 No.3/4, pp.170 - 201

Published online: 20 Jan 2010 *

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