Levan Giorgashvili, Ketevan Skhvitaridze

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

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.

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

MSC 2000: 35J55, 74H420, 74H25