Explicit solutions of the boundary value problems of the theory of consolidation with double porosity for the half-plane
-
Mikheil Basheleishvili
and
Lamara Bitsadze
Abstract.
The purpose of this paper is to consider a two-dimensional version of the Aifantis equation of statics of the theory of consolidation with double porosity and effectively solve the basic BVPs for the half-plane. We extend the potential method and the theory of integral equations to BVPs of the theory of consolidation with double porosity. For all problems, we construct Fredholm type integral equations. For the Aifantis equation of statics we construct a particular solution and reduce the solution of the basic BVPs of the theory of consolidation with double porosity to the solution of the basic BVPs for the equation for an isotropic body. A Poisson type formula is constructed for the solution of the first and of the second boundary value problem for the half-plane.
© 2012 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- Stability estimates for the multidimensional elliptic obstacle problem
- On the two-point boundary value problems for linear impulsive systems with singularities
- Explicit solutions of the boundary value problems of the theory of consolidation with double porosity for the half-plane
- Convergence of modification of the Durrmeyer type -Baskakov operators
- Backward stochastic differential equations with a convex generator
- On some ideal defined by density topology in the Cantor set
- Maximal operator of the Fejér means of triangular partial sums of two-dimensional Walsh–Fourier series
- Fixed point theorems for hybrid mappings satisfying an integral type contractive condition
- On the nonexistence of blowing-up solutions to a fractional functional-differential equation
- Two-weight inequalities for multilinear maximal operators
- An asymptotic model of a nonlinear adaptive orthotropic elastic rod
- Approximation of functions on locally compact abelian groups
