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.
Citation:
A. M. Meirmanov, “Acoustic and filtration properties of a thermoelastic porous medium: Biot's equations of thermo-poroelasticity”, Sb. Math., 199:3 (2008), 361–384
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\by A.~M.~Meirmanov
\paper Acoustic and filtration properties of a~thermoelastic porous medium: Biot's equations of thermo-poroelasticity
\jour Sb. Math.
\yr 2008
\vol 199
\issue 3
\pages 361--384
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Linking options:
https://www.mathnet.ru/eng/sm3818
https://doi.org/10.1070/SM2008v199n03ABEH003924
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This publication is cited in the following 6 articles:
A. S. Shamaev, V. V. Shumilova, “Spectrum of One-Dimensional Eigenoscillations of a Medium Consisting of Viscoelastic Material with Memory and Incompressible Viscous Fluid”, J Math Sci, 257:5 (2021), 732
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
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
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
A. M. Meirmanov, “Derivation of the equations of nonisothermal acoustics in elastic porous media”, Siberian Math. J., 51:1 (2010), 128–143
Meirmanov A., “Double porosity models for liquid filtration in incompressible poroelastic media”, Math. Models Methods Appl. Sci., 20:4 (2010), 635–659
Citation in format AMSBIB
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