M. Basheleishvili and L. Bitsadze
abstract:
The purpose of this paper is to consider three-dimensional version of Aifantis'
equations of statics of the theory of consolidation with double porosity and to
study the uniqueness and existence of solutions of basic boundary value problems
(BVPs). In this work we intend to extend the potential method and the theory of
integral equation to BVPs of the theory of consolidation with double porosity.
Using these equations, the potential method and generalized Green's formulas, we
prove the existence and uniqueness theorems of solutions for the first and
second BVPs for bounded and unbounded domains. For Aifantis' equation of statics
we construct one particular solution and we reduce the solution of basic BVPs of
the theory of consolidation with double porosity to the solution of the basic
BVPs for the equation of an isotropic body.
Mathematics Subject Classification: 74G25,74G30
Key words and phrases: Porous media, double porosity, consolidation, fundamental solution