Journal of Mathematical Sciences

, Volume 206, Issue 4, pp 371–392 | Cite as

Basic Boundary-Value Problems for a Solid Body with Double Porosity and Two Nonintersecting Spherical Cavities

  • L. GiorgashviliEmail author
  • G. Karseladze
  • M. Kharashvili


In this paper, we examine the basic boundary-value problems for a three-dimensional space filled with a solid body having double porosity and two nonintersecting spherical cavities. We search for a solution of the problem by using the representation of a general solution of a system of homogeneous differential equations of statics, which is expressed in terms of four harmonic and one metaharmonic functions. The solution of the problem is reduced to the investigation of an infinite system of linear algebraic equations. It is shown that the obtained system is of normal type. Solutions of the considered problems are obtained in the form of absolutely and uniformly convergent series.


Solid Body Neumann Problem Linear Algebraic Equation Homogeneous Problem Convergent Series 
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© Springer Science+Business Media New York 2015

Authors and Affiliations

  • L. Giorgashvili
    • 1
    Email author
  • G. Karseladze
    • 1
  • M. Kharashvili
    • 1
  1. 1.Department of MathematicsGeorgian Technical UniversityTbilisiGeorgia

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