Georgian Mathematical Journal 13 (2006), No. 1, 035--053
Copyright Heldermann Verlag 2006
Solution of a Nonclassical Problem of Oscillation of Two-Component Mixtures
Levan Giorgashvili
Higher Mathematics Chair No. 99, Georgian Technical University, 77 M. Kostava St., Tbilisi 0175, Georgia
lgiorgashvili@yahoo.com
Ketevan Skhvitaridze
Higher Mathematics Chair No. 99, Georgian Technical University, 77 M. Kostava St., Tbilisi 0175, Georgia
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: 35J55, 74H420, 74H25
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