Several Results on Uniqueness and Continuous Data Dependence in Thermoelasticity of Type III

Abstract

In the present paper we consider the linear theory of thermoelasticity of type III for anisotropic and inhomogeneous materials as developed by Green and Naghdi (1992, 1995). We consider the general initial-boundary value problems associated with the theory in concern and then we identify some mild constitutive hypotheses that lead to appropriate energetic measures of solutions. On this basis we are able to prove some new uniqueness and continuous data dependence theorems. When the boundary surface is maintained at zero thermal displacement, we are able to obtain uniqueness and continuous data dependence results by using only the positiveness of the density mass, the positive definiteness of the elasticity tensor and the positive definiteness of the heat conductivity tensor, without any sign defined assumption upon the specific heat. These results are established by means of new techniques which are essentially different from those previously used for the classical theory of thermoelasticity.