**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

**abstract:**

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