A new uniqueness theorem of the linear thermo-elastic dynamics on unbounded domains

Abstract

In the present paper, the uniqueness of the solution to the initial boundary value problem of the linear thermo-elastic dynamics on unbounded domains is obtained under less restrictive conditions, including abandoning the positive semi-definiteness of the elasticity tensor and boundness of the material tensor and restrictions on the acoustic tensor and the coupled tensor, and the results in [1] are refined. The conclusion here is valid for the case on bounded domains and the linear elastic dynamics on unbounded domains, hence the results in [2–4] are refined too. Abandoning the positive semi-definiteness of elasticity tensor permits that the uniqueness of the kinetic process is still valid for deformation of the wider materials, especially for the case that there are phase-transition during deformation process provided that the constitutive equations are unchanged in forms.