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

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).