Potential method in the linear theory of triple porosity thermoelasticity

In this paper the linear theory of triple porosity thermoelasticity is considered and the basic internal and external boundary value problems (BVPs) of steady vibrations are investigated. Indeed, Green's identities are obtained and the Sommerfeld-Kupradze type radiation conditions are established. The surface (single-layer and double-layer) and volume potentials are constructed and their basic properties are given. The BVPs are reduced to the always solvable singular integral equations for which Fredholm's theorems are valid. Finally, the existence and uniqueness theorems for classical solutions of the basic BVPs of steady vibrations are proved by means of the potential method (boundary integral equation method) and the theory of singular integral equations.