Potential method in the theory of Moore-Gibson-Thompson thermoporoelasticity

Abstract

In the present paper the linear theory of Moore–Gibson–Thompson thermoporoelasticity is considered and the basic boundary value problems (BVPs) of steady vibrations are investigated. Namely, the fundamental solution of the system of steady vibration equations are constructed explicitly by elementary functions and its basic properties are established. The formula of integral representation of regular vectors is obtained. The surface and volume potentials are introduced and their basic properties are given. Then, some helpful singular integral operators are defined for which the symbolic determinants and indexes are calculated. The BVPs of steady vibrations are reduced to the equivalent singular integral equations. Finally, the existence theorems for classical solutions of the aforementioned BVPs are proved with the help of the potential method and the theory of singular integral equations.