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

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.