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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2016, Volume 13, Pages 49–74
DOI: https://doi.org/10.17377/semi.2016.12.005
(Mi semr656)
 

This article is cited in 1 scientific paper (total in 1 paper)

Differentical equations, dynamical systems and optimal control

The homogenized models of the isothermal acoustics in the configuration «fluid–poroelastic medium»

A. M. Meirmanov, S. A. Gritsenko, A. A. Gerus

Belgorod state national research University, Pobedy, 85, 308015, Belgorod, Russia
Full-text PDF (686 kB) Citations (1)
References:
Abstract: We consider a mathematical model of the isothermal acoustics in composite medium with two different components: liquid region and the elastic body perforated by a system of pores, filled the same liquid. The model is based on the classical axioms of continuum mechanics and contains rapidly oscillating coefficients that depend on a small parameter. Such a model, although precise enough, cannot, however, be used for numerical calculations. The problem is solved by using homogenization, i. e. the derivation of the equations not containing rapidly oscillating coefficients. Separately for the fluid and separately for poroelastic medium results already obtained previously. In this configuration of the two-component medium the main problem is the conditions of continuity at the common boundary between the liquid region and poroelastic region. In the present work are displayed six homogenized models of different complexity with the various coefficients characterizing the medium.
Keywords: composite medium, periodic structure, isothermal Stokes equations, acoustic equation, poro-elasticity, homogenization of periodic structures, two-scale convergence.
Funding agency Grant number
Russian Science Foundation 14-17-00556
Received June 26, 2015, published February 11, 2016
Document Type: Article
UDC: 517.958
MSC: 35B27
Language: Russian
Citation: A. M. Meirmanov, S. A. Gritsenko, A. A. Gerus, “The homogenized models of the isothermal acoustics in the configuration «fluid–poroelastic medium»”, Sib. Èlektron. Mat. Izv., 13 (2016), 49–74
Citation in format AMSBIB
\Bibitem{MeiGriGer16}
\by A.~M.~Meirmanov, S.~A.~Gritsenko, A.~A.~Gerus
\paper The homogenized models of the isothermal acoustics in the configuration <<fluid--poroelastic medium>>
\jour Sib. \`Elektron. Mat. Izv.
\yr 2016
\vol 13
\pages 49--74
\mathnet{http://mi.mathnet.ru/semr656}
\crossref{https://doi.org/10.17377/semi.2016.12.005}
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  • This publication is cited in the following 1 articles:
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    Full-text PDF :77
    References:76
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