The Cauchy problem for the linear hyperbolic equations system of the theory of thermoelasticity of the temperature rate - dependent solids (Q1093398)

Existence, uniqueness and regularity theorems for a displacement- temperature initial-value problem of linear anisotropic nonhomogeneous temperature-rate dependent thermoelasticity in which the heat flux is a linear function of the temperature-rate (the case of violation of the Fourier law) are formulated. The three limiting cases of the theory are discussed: 1. A rigid heat conductor; 2. A body in which thermomechanical coupling is ignored; 3. A thermoelastic body. For these cases pertinent theorems are given. Proofs of the theorems, based on a theory of pseudodifferential operators and first-order symmetric hyperbolic systems, are omitted in the article.