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Mat. Sb., 2008, Volume 199, Number 3, Pages 45–68 (Mi msb3818)  

This article is cited in 5 scientific papers (total in 5 papers)

Acoustic and filtration properties of a thermoelastic porous medium: Biot's equations of thermo-poroelasticity

A. M. Meirmanov

Belgorod State University

Abstract: A linear system of differential equations describing the joint motion of a thermoelastic porous body and an incompressible thermofluid occupying a porous space is considered. Although the problem is linear, it is very hard to tackle due to the fact that its main differential equations involve non-smooth rapidly oscillating coefficients, inside the differentiatial operators. A rigorous substantiation based on Nguetseng's two-scale convergence method is carried out for the procedure of the derivation of homogenized equations (not containing rapidly oscillating coefficients), which for different combinations of the physical parameters can represent Biot's system of equations of thermo-poroelasticity, the system consisting of Lamé's non-isotropic equations of thermoelasticity for the solid component and the acoustic equations for the fluid component of a two-temperature two-velocity continuum, or Lamé's non-isotropic thermoelastic system for a two-temperature one-velocity continuum.
Bibliography: 16 titles.

DOI: https://doi.org/10.4213/sm3818

Full text: PDF file (620 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2008, 199:3, 361–384

Bibliographic databases:

UDC: 517.958:531.72+517.958:539.3(4)
MSC: 35Q72, 74Q10, 74B05, 76M50, 76S05
Received: 11.12.2006 and 13.07.2007

Citation: A. M. Meirmanov, “Acoustic and filtration properties of a thermoelastic porous medium: Biot's equations of thermo-poroelasticity”, Mat. Sb., 199:3 (2008), 45–68; Sb. Math., 199:3 (2008), 361–384

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    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
    2. Meirmanov A., “Double porosity models for liquid filtration in incompressible poroelastic media”, Math. Models Methods Appl. Sci., 20:4 (2010), 635–659  crossref  mathscinet  zmath  isi  elib  scopus
    3. A. M. Meirmanov, “Prilozhenie metoda povtornogo usredneniya differentsialnykh uravnenii v teorii filtratsii szhimaemykh vyazkikh zhidkostei v szhimaemykh treschinovato-poristykh sredakh. Chast I: Mikroskopicheskoe opisanie”, Matem. modelirovanie, 23:1 (2011), 100–114  mathnet  mathscinet
    4. V. V. Vlasov, N. A. Rautian, A. S. Shamaev, “Spectral analysis and correct solvability of abstract integrodifferential equations arising in thermophysics and acoustics”, Journal of Mathematical Sciences, 190:1 (2013), 34–65  mathnet  crossref  mathscinet
    5. A. M. Meirmanov, O. V. Galtsev, S. A. Gritsenko, “On homogenized equations of filtration in two domains with common boundary”, Izv. Math., 83:2 (2019), 330–360  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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