M. Basheleishvili and L. Bitsadze
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