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Sibirsk. Mat. Zh., 2010, Volume 51, Number 1, Pages 156–174 (Mi smj2074)  

This article is cited in 4 scientific papers (total in 4 papers)

Derivation of the equations of nonisothermal acoustics in elastic porous media

A. M. Meirmanov

Belgorod State University, Belgorod

Abstract: We consider the problem of the joint motion of a thermoelastic solid skeleton and a viscous thermofluid in pores, when the physical process lasts for a few dozens of seconds. These problems arise in describing the propagation of acoustic waves. We rigorously derive the homogenized equations (i.e., the equations not containing fast oscillatory coefficients) which are different types of nonclassical acoustic equations depending on relations between the physical parameters and the homogenized heat equation. The proofs are based on Nguetseng's two-scale convergence method.

Keywords: nonisothermal Stokes and Lamé's equations, equations of acoustics, two-scale convergence, homogenization of periodic structures.

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English version:
Siberian Mathematical Journal, 2010, 51:1, 128–143

Bibliographic databases:

UDC: 517.958:531.72+517.958:539.3(4)
Received: 21.10.2007
Revised: 05.05.2009

Citation: A. M. Meirmanov, “Derivation of the equations of nonisothermal acoustics in elastic porous media”, Sibirsk. Mat. Zh., 51:1 (2010), 156–174; Siberian Math. J., 51:1 (2010), 128–143

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. V. Nekrasova, “Nekotorye modeli gidravlicheskogo udara v neftyanom plaste”, Sib. zhurn. industr. matem., 14:3 (2011), 79–86  mathnet  mathscinet
    2. A. M. Meirmanov, I. V. Nekrasova, “Mathematical models of a hydraulic shock in a slightly viscous liquid”, Math. Models Comput. Simul., 4:6 (2012), 597–610  mathnet  crossref  mathscinet  elib
    3. A. A. Gerus, S. A. Gritsenko, “Usrednenie matematicheskoi modeli akustiki”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 15:3 (2015), 264–272  mathnet  crossref  elib
    4. A. A. Gerus, S. A. Gritsenko, A. M. Meirmanov, “The deduction of the homogenized model of isothermal acoustics in a heterogeneous medium in the case of two different poroelastic domains”, J. Appl. Industr. Math., 10:2 (2016), 199–208  mathnet  crossref  crossref  mathscinet  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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