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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, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

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1572-9176
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Volume 19, Issue 1 (Jan 2012)

Issues

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

Mikheil Basheleishvili
  • I. Vekua Institute of Applied Mathematics, I. Javakhishvili Tbilisi State University, 2 University St., Tbilisi 0186, Georgia
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/ Lamara Bitsadze
Published Online: 2012-02-29 | DOI: https://doi.org/10.1515/gmj-2012-0002

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.

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

About the article

Received: 2010-12-28

Published Online: 2012-02-29

Published in Print: 2012-03-01


Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2012-0002.

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© 2012 by Walter de Gruyter Berlin Boston. Copyright Clearance Center

Citing Articles

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[1]
Lamara Bitsadze and Natela Zirakashvili
Advances in Mathematical Physics, 2016, Volume 2016, Page 1
[2]
L. Giorgashvili, D. Burchuladze, and K. Skhvitaridze
Journal of Mathematical Sciences, 2016, Volume 216, Number 4, Page 538

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