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Tr. Mat. Inst. Steklova, 2008, Volume 261, Pages 210–219 (Mi tm749)  

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

Nonisothermal Filtration and Seismic Acoustics in Porous Soil: Thermoviscoelastic Equations and Lamé Equations

A. M. Meirmanov

Belgorod State University

Abstract: We consider a linear system of differential equations that describes the joint motion of an incompressible elastic porous body and an incompressible fluid filling the pores. The model is very complicated because the main differential equations contain the derivatives of expressions with nondifferentiable rapidly oscillating small and large coefficients. On the basis of Nguetseng's two-scale convergence method, we derive homogenized equations in a rigorous way; depending on the geometry of pores, these are either the thermoviscoelasticity equations (for a connected porous space) or the anisotropic thermoelastic Lamé system.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2008, 261, 204–213

Bibliographic databases:

UDC: 517.958:531.72+517.958:539.3(4)
Received in January 2007

Citation: A. M. Meirmanov, “Nonisothermal Filtration and Seismic Acoustics in Porous Soil: Thermoviscoelastic Equations and Lamé Equations”, Differential equations and dynamical systems, Collected papers, Tr. Mat. Inst. Steklova, 261, MAIK Nauka/Interperiodica, Moscow, 2008, 210–219; Proc. Steklov Inst. Math., 261 (2008), 204–213

Citation in format AMSBIB
\Bibitem{Mei08}
\by A.~M.~Meirmanov
\paper Nonisothermal Filtration and Seismic Acoustics in Porous Soil: Thermoviscoelastic Equations and Lam\'e Equations
\inbook Differential equations and dynamical systems
\bookinfo Collected papers
\serial Tr. Mat. Inst. Steklova
\yr 2008
\vol 261
\pages 210--219
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\zmath{https://zbmath.org/?q=an:06014619}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2008
\vol 261
\pages 204--213
\crossref{https://doi.org/10.1134/S0081543808020156}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-48849084501}


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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. A. M. Meirmanov, “Derivation of the equations of nonisothermal acoustics in elastic porous media”, Siberian Math. J., 51:1 (2010), 128–143  mathnet  crossref  mathscinet  isi  elib  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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