Uniqueness and decay in local thermal non‐equilibrium double porosity thermoelasticity

Abstract

This paper studies a model for thermoelasticity where the body has a double porosity structure. There are the usual pores associated to a porous body, herein called macro pores. In addition, the solid skeleton contains cracks or fissures that give rise to a micro porosity. The fully anisotropic situation is analyzed. We firstly establish uniqueness of a solution to the boundary‐initial value problem when the elastic coefficients are sign indefinite and are required to satisfy only major symmetry. Furthermore, in the quasi‐equilibrium case, where the solid acceleration is neglected, we demonstrate that a solution to the boundary‐initial value problem with zero boundary conditions will decay to zero in a certain sense, under the assumption that there are no sources and external body force involved.