Representation Formula for General Solution of a Homogeneous System of Differential Equations

Abstract

We consider the stationary oscillation case of the theory of linear thermoelasticity with microtemperatures of materials. 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. These formulas are very convenient and useful in many particular problems for domains with concrete geometry. Here we demonstrate applications of these formulas to the Dirichlet- and Neumann-type boundary-value problems for a ball. Uniqueness theorems are proved. We construct explicit solutions in the form of absolutely and uniformly convergent series.