Potential method in the theory of micropolar viscoelasticity

Author: Maia Svanadze
Keywords: Potential method, theory of micropolar viscoelasticity
Annotation:

In this talk the linear theory of micropolar viscoelasticity for Kelvin-Voigt materials is considered. The fundamental solution of the system of equations of steady vibrations is constructed by means of elementary functions and its basic properties are established. The Green’s formulas and integral representations of Somigliana type of regular vector and classical solution are obtained. The uniqueness theorems of the internal and external basic boundary value problems (BVPs) of steady vibrations are proved. The basic properties of surface and volume potentials are given. Finally, the existence theorems for classical solutions of the above mentioned BVPs are proved by using the potential method and the theory of singular integral equations.