POTENTIAL METHOD IN THE THEORY OF THERMOVISCOELASTICITY FOR MATERIALS WITH VOIDS

摘要

In the present article, the linear theory of thermoviscoelasticity for Kelvin-Voigt materials with voids is considered. The Sommerfeld-Kupradze type radiation conditions are established. The uniqueness theorems of the internal and external basic boundary value problems (BVPs) of steady vibrations are proved. The Green's formulas and integral representations of Somigliana type of regular vector and classical solution are obtained. The basic properties of thermoelastopotentials and singular integral operators are given. Finally, the existence theorems for classical solutions of the above mentioned BVPs are proved by using the potential method (boundary integral method) and the theory of singular integral equations.