**Lamara Bitsadze**

##
Explicit Solution of the First BVP of the Elastic Mixture for Half-Space

**abstract:**

We consider the first BVP of elastic mixture theory for a
transversally-isotropic half-space. The solution of the first BVP for the
transversally-isotropic half-space is given in [V. D. Kupradze, T. G. Gegelia,
M. O. Basheleishvili, and T. V. Burchuladze, Three-dimensional problems of the
mathematical theory of elasticity and thermoelasticity. Translated from the
second Russian edition. Edited by V. D. Kupradze. *North-Holland Series in
Applied Mathematics and Mechanics,* 25.*North-Holland Publishing Co.,
Amsterdam-New York,* 1979]. The present paper is an attempt to use this
result for the BVP of elastic mixture theory for a transversally-isotropic
elastic body. Using the potential method and the theory of integral equations,
the uniqueness theorem is proved for a half-space and the first BVP previously
is solved effectively (in quadratures), which has not been solved.

**Mathematics Subject Classification:**
74E30, 74G05

**Key words and phrases:** Elastic mixture, uniqueness theorem, potential
method, explicit solution