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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board Member: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, J. / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

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Explicit solutions of the boundary value problems of the theory of consolidation with double porosity for the half-plane

1I. Vekua Institute of Applied Mathematics, I. Javakhishvili Tbilisi State University, 2 University St., Tbilisi 0186, Georgia

2Ilia State University, 32, I. Chavchavadze Ave., Tbilisi, 0179, Georgia

Citation Information: Georgian Mathematical Journal. Volume 19, Issue 1, Pages 41–48, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: 10.1515/gmj-2012-0002, February 2012

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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.

Keywords.: Porous media; double porosity; consolidation; fundamental solution

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