Fundamental solution and uniqueness theorems in the linear theory of thermoviscoelasticity for solids with double porosity

摘要

In this article, the linear theory of thermoviscoelasticity for Kelvin-Voigt materials with double porosity is considered. The fundamental solution of the system of equations of steady vibrations is constructed by elementary functions and its basic properties are established. The Green's first identity in the considered theory is obtained. A wide class of the internal and external boundary value problems (BVPs) of steady vibrations is formulated. Finally, on the basis of the Green's identity, the uniqueness theorems for regular (classical) solutions of these BVPs are proved.