**Levan Giorgashvili, Ketevan Skhvitaridze**

## Solution of a
Nonclassical Problem of Oscillation of Two-Component Mixtures

**Abstract:**

A general representation of solutions by six metaharmonic functions is obtained
for a system of homogeneous equations of oscillation of two-component mixtures.
The boundary value problem of oscillation of two-component mixtures is
investigated when the normal components of partial displacement vectors and the
tangent components of partial rotation vectors are given on the boundary.
Uniqueness theorems of the considered problem are proved. Solutions are obtained
in terms of absolutely and uniformly convergent series.

**Keywords:**

Elasticity theory, mixture theory, continual theory of mixtures, mataharmonic
function, radiation condition.

**MSC 2000:** 35J55, 74H420, 74H25