Uniqueness theorems about high-order time differential thermoelastic models

Abstract

The purpose of the present manuscript is to investigate the well-posedness question for three different stand-alone and self-consistent thermoelastic models derived from the time differential formulation of the dual-phase-lag heat conduction law and characterized by Taylor expansion orders higher than those most commonly considered in literature up to now. The main motivation at the basis of this study is that the interaction among multiple energy carriers progressively gains significance as the observation scales reduce and has, as a direct consequence, the involvement of high-order terms in the time differential dual-phase-lag heat conduction constitutive equation. Considering inhomogeneous and anisotropic linear thermoelastic materials, we are able to prove three uniqueness results through the use of appropriate integral operators and Lagrange identities; the results are proved without any restriction imposed on the delay times other than their positivity.