L. Giorgashvili, M. Kharashvili, K. Skhvitaridze, and E. Elerdashvili

Boundary Value Problems of the Theory of Thermoelasticity with Microtemperatures for Domains Bounded by a Spherical Surface

We consider the stationary oscillation case of the theory of linear thermoelasticity of materials with microtemperatures. The representation formula of a general solution of the homogeneous system of differential equations obtained in the paper is expressed by means of seven metaharmonic functions. This formula is very convenient and useful in many particular problems for domains with concrete geometry. Here we demonstrate an application of this formulas to the Dirichlet and Neumann type boundary value problem for a ball. The uniqueness theorems are proved. An explicit solutions in the form of absolutely and uniformly convergent series are constructed.

Mathematics Subject Classification: 74A15, 74B10, 74F20

Key words and phrases: Microtemperature, thermoelasticity, Fourier-Laplace series, stationary oscillation