Geodesic
Darcy's law in anisothermic porous medium
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 141-154.

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A linear system of differential equations describing a joint motion of thermoelastic porous body with sufficiently large Lame's constants (absolutely rigid body) and thermofluid occupying porous space is considered. The rigorous justification is fulfilled for homogenization procedures as the dimensionless size of the pores tends to zero, while the porous body is geometrically periodic. As the results, we derive decoupled system consisting of Darcy's system of filtration for thermofluid (first approximation) and anisotropic Lamé's system of equations for thermoelastic solid (second approximation). The proof is based on Nguetseng's two-scale convergence method of homogenization in periodic structures. 
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A. M. Meirmanov. Darcy's law in anisothermic porous medium. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 4 (2007), pp. 141-154. http://geodesic.mathdoc.fr/item/SEMR_2007_4_a10/

[1] A. M. Meirmanov, S. A. Sazhenkov, Generalized solutions to the linearized equations of thermoelastic solid and viscous thermofluid, 12 Nov 2006, arXiv: math/0611350 | MR

[2] G. Nguetseng, “A general convergence result for a functional related to the theory of homogenization”, SIAM J. Math. Anal., 20 (1989), 608–623 | DOI | MR | Zbl

[3] D. Lukkassen, G. Nguetseng, P. Wall, “Two-scale convergence”, Int. J. Pure and Appl. Math., 2:1 (2002), 35–86 | MR | Zbl

[4] R. Burridge, J. B. Keller, “Poroelasticity equations derived from microstructure”, J. Acoust. Soc. Am., 70:4 (1981), 1140–1146 | DOI | Zbl

[5] E. Sanches-Palensiya, Neodnorodnye sredy i teoriya vibratsii, Mir, Moskva, 1984 | MR

[6] G. Nguetseng, “Asymptotic analysis for a stiff variational problem arising in mechanics”, SIAM J. Math. Anal., 21 (1990), 1394–1414 | DOI | MR | Zbl

[7] R. P. Gilbert, A. Mikelić, “Homogenizing the acoustic properties of the seabed: Part I”, Nonlinear Analysis, 40 (2000), 85–212 | DOI | MR

[8] Th. Clopeau, J. L. Ferrin, R. P. Gilbert, A. Mikelić, “Homogenizing the acoustic properties of the seabed: Part II”, Mathematical and Computer Modelling, 33 (2001), 821–841 | DOI | MR | Zbl

[9] J. L. Ferrin, A. Mikelić, “Homogenizing the acoustic properties of a porous matrix containing an incompressible inviscid fluids”, Math. Meth. Appl. Sci., 26 (2003), 831–859 | DOI | MR | Zbl

[10] A. M. Meirmanov, Nguetseng's two-scale convergence method for filtration and seismic acoustic problems in elastic porous media, 11 Nov 2006, arXiv: math/0611330

[11] E. Acerbi, V. Chiado Piat, G. Dal Maso, D. Percivale, “An extension theorem from connected sets and homogenization in general periodic domains”, Nonlinear Anal., 18 (1992), 481–496 | DOI | MR | Zbl

[12] V. V. Zhikov, S. M. Kozlov, O. A. Oleinik, Usrednenie differentsialnykh operatorov, Nauka, Moskva, 1993 | MR | Zbl

[13] O. A. Ladyzhenskaya, Matematicheskie voprosy dinamiki vyazkoi neszhimaemoi zhidkosti, Nauka, Moskva, 1970 | MR