L. Giorgashvili, G. Karseladze, G. Sadunishvili

Solution of a Boundary Value Problem of Statics of Two-Component Elastic Mixtures for a Space with Two Nonintersecting Spherical Cavities

Using a general representation of solutions of a system of homogeneous differential equations of statics of two-component elastic mixtures which is expressed by six harmonic functions, we study boundary value problems of statics of two-component elastic mixtures for a space with two nonintersecting spherical cavities when different boundary conditions are given on the spherical surfaces. The uniqueness theorems are proved. The solution of the considered problems is reduced to the investigation of an infinite system of linear algebraic equations. It is proved that such systems are quasiregular. The question of regularity of the partial displacement vector is studied.

Mathematics Subject Classification: 35J55, 75H20, 74H25

Key words and phrases: Elasticity theory, theory of mixtures, Green's formula, regular functions