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Advances in Mathematical Physics
Volume 2014, Article ID 473068, 4 pages
Research Article

Fundamental Solutions for Periodic Media

Institute for Problems in Mechanics, Moscow 119526, Russia

Received 7 October 2014; Revised 27 November 2014; Accepted 1 December 2014; Published 14 December 2014

Academic Editor: Nikos Mastorakis

Copyright © 2014 Sergey V. Kuznetsov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Necessity for the periodic fundamental solutions arises when the periodic boundary value problems should be analyzed. The latter are naturally related to problems of finding the homogenized properties of the dispersed composites, porous media, and media with uniformly distributed microcracks or dislocations. Construction of the periodic fundamental solutions is done in terms of the convergent series in harmonic polynomials. An example of the periodic fundamental solution for the anisotropic porous medium is constructed, along with the simplified lower bound estimate.