High-order effects of thermal lagging in deformable conductors

The purpose of the present paper is to investigate about the well-posedness question for a thermoelastic model describing the intrinsic coupling between the high-order lagging behavior and the ultrafast deformation. The main motivation behind 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 dual-phase-lag constitutive equation for the heat flux. Moreover, the ultrafast deformation can occur in times comparable to the characteristic times in phonon-electron interactions that are due to hot-electron blast and thermal expansion of the lattices. Considering an inhomogeneous and anisotropic linear thermoelastic medium, we are able to prove the uniqueness and continuous dependence results through the use of appropriate integral operators entering into the constitutive equations and Lagrange identities and the time weighted function method, provided very mild assumptions are supposed upon the thermoelastic characteristics.