M. Basheleishvili and L. Bitsadze

Two-Dimensional Boundary Value Problems of the Theory of Consolidation with Double Porosity

abstract:
The purpose of this paper is to consider two-dimensional version of quasistatic Aifantis' equation of the theory of consolidation with double porosity and to study the uniqueness and existence of solutions of basic boundary value problems (BVPs). The fundamental and some other matrices of singular solutions are constructed in terms of elementary functions for the steady-state quasistatic equations of the theory of consolidation with double porosity. Using the fundamental matrix we construct the simple and double layer potentials and study their properties near the boundary. Using these potentials, for the solution of the first basic BVP we construct Fredholm type integral equation of the second kind and prove the existence theorem of solution for the finite and infinite domains.

Mathematics Subject Classification: 74G25, 74G30

Key words and phrases: Steady-state quasistatic equations, porous media, double porosity, fundamental solution