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30.01.2020 | Original Paper | Ausgabe 5/2020

Acta Mechanica 5/2020

Potential method in the linear theory of viscoelastic porous mixtures

Zeitschrift:
Acta Mechanica > Ausgabe 5/2020
Autor:
Maia M. Svanadze
Wichtige Hinweise
This work was supported by Shota Rustaveli National Science Foundation (SRNSF) [Project \(\#\) YS-18-610].

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Abstract

In the present paper, the linear theory of viscoelasticity for binary porous mixtures is considered. The fundamental solution of the system of steady vibration equations is constructed, and its basic properties are established. Green’s identities of this theory are obtained. The uniqueness theorems for classical solutions of the internal and external basic boundary value problems (BVPs) of steady vibrations are proved. The surface and volume potentials are introduced, and their basic properties are established. The determinants of symbolic matrices of the singular integral operators are calculated explicitly, and the BVPs are reduced to the always solvable singular integral equations for which Fredholm’s theorems are valid. Finally, the existence theorems for classical solutions of the internal and external BVPs of steady vibrations are proved by means of the potential method and the theory of singular integral equations.

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