Linear coupled theory of viscoelasticity for triple-porosity materials is considered and the basic internal and external boundary value problems (BVPs) of steady vibrations are investigated. Namely, the fundamental solution of the system of steady vibration equations of the considered theory is constructed. The uniqueness theorems for the classical solutions of the BVPs of steady vibrations are proved. The surface (single-layer and double-layer) and volume potentials are constructed and their basic properties are established. The BVPs are reduced to the always solvable singular integral equations. Finally, the existence theorems for classical solutions of the internal and external BVPs of steady vibrations are proved by means of the potential method.

Project members:

• Merab Svanadze (Principal Investigator)

• Maia Svanadze (Coordinator)