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 J. Sib. Fed. Univ. Math. Phys., 2015, Volume 8, Issue 3, Pages 356–370 (Mi jsfu439)

Homogenization of acoustic equations for a partially perforated elastic material with slightly viscous fluid

Alexey S. Shamaev, Vladlena V. Shumilova

Institute for Problems in Mechanics of RAS, Vernadskogo, 101–1, Moscow, 119526, Russia

Abstract: In this paper a mathematical model describing small oscillations of a heterogeneous medium is considered. The medium consists of a partially perforated elastic material and a slightly viscous compressible fluid filling the pores. For the given model the corresponding homogenized problem is constructed by using the two-scale convergence method. The boundary conditions connecting equations of the homogenized model on the boundary between the continuous elastic material and the porous elastic material with fluid are found.

Keywords: homogenization, two-scale convergence, heterogeneous medium.

DOI: https://doi.org/10.17516/1997-1397-2015-8-3-356-370

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UDC: 517.958
Accepted: 25.06.2015
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Citation: Alexey S. Shamaev, Vladlena V. Shumilova, “Homogenization of acoustic equations for a partially perforated elastic material with slightly viscous fluid”, J. Sib. Fed. Univ. Math. Phys., 8:3 (2015), 356–370

Citation in format AMSBIB
\Bibitem{ShaShu15} \by Alexey~S.~Shamaev, Vladlena~V.~Shumilova \paper Homogenization of acoustic equations for a partially perforated elastic material with slightly viscous fluid \jour J. Sib. Fed. Univ. Math. Phys. \yr 2015 \vol 8 \issue 3 \pages 356--370 \mathnet{http://mi.mathnet.ru/jsfu439} \crossref{https://doi.org/10.17516/1997-1397-2015-8-3-356-370}