Uniqueness Theorems in the Quasi-static Theory of Thermoelasticity for Solids with Double Porosity

In this paper the linear quasi-static theory of thermoelasticity for solids with double porosity is considered. The system of equations of this theory is based on the equilibrium equations for solids with double porosity, conservation of fluid mass, constitutive equations, Darcy’s law for materials with double porosity and Fourier’s law for heat conduction. A wide class of the internal and external boundary value problems (BVPs) are formulated. The Green’s formulas in the considered theory are obtained. The formulas of integral representations of regular vector and regular (classical) solutions are established, and finally, the uniqueness theorems for classical solutions of the above mentioned BVPs are proved.