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Singular limit of a two-phase flow problem in porous medium as the air viscosity tends to zero

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  • In this paper we consider a two-phase flow problem in porous media and study its singular limit as the viscosity of the air tends to zero; more precisely, we prove the convergence of subsequences to solutions of a generalized Richards model.
    Mathematics Subject Classification: 35K65, 35D30, 35B25.


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  • [1]

    H. W. Alt and S. Luckhaus, Quasilinear elliptic equations, Math.-Z., 183 (1983), 311-341.doi: 10.1007/BF01176474.


    H. Brezis, "Analyse Fonctionnelle Théorie et Applications,'' Masson, (1993).


    Z. Chen, Degenerate two-phase incompressible flow. I. Existence, uniqueness and regularity of a weak solution, J. Differential Equations, 171 (2001), 203-232.doi: 10.1006/jdeq.2000.3848.


    F. Z. Daïm, R. Eymard and D. Hilhorst, Existence of a solution for two phase flow in porous media: the case that the porosity depends on the pressure, J. Math. Anal. Appl., 326 (2007), 332-351.doi: 10.1016/j.jmaa.2006.02.082.


    C. J. Van Duijn and L. A. Peletier, Nonstationary filtration in partially satured porous media, Arch. Rational Mech. Anal., 78 (1982), 173-198.doi: 10.1007/BF00250838.


    R. Eymard, M. Gutnic and D. Hilhorst, The finit volume method for an elliptic-parabolic equation, Acta Mathematica Universitatis Comenianae, 67 (1998), 181-195.


    J. Hulshof and N. Wolanski, Monotone flows in n-dimensional partially saturated porous media: Lipschitz-continuity of the interface, Arch. Rational Mech. Anal., 102 (1988), 287-305.doi: 10.1007/BF00251532.


    O. A. Ladyhenskaya and N. N. Ural'ceva, "Linear and Quasilinear Elliptic Equations,'' American Mathematical Society, (1964).


    O. A. Ladyhenskaya, V. A. Solonnikov and N. N. Ural'ceva, "Linear and Quasilinear Equations of Parabolic Type,'' American Mathematical Society, 1968.


    F. Otto, $L^1$-concentration and uniqueness for quasilinear elliptic-parabolic equations, J. Differential Equations, 131 (1996), 20-38.doi: 10.1006/jdeq.1996.0155.


    I. S. Pop, Error estimates for a time discretization method for the Richard's equation, Computational Geosciences, 6 (2002), 141-160.doi: 10.1023/A:1019936917350.


    F. A. Radu, I. S. Pop and P. Knabner, Order of convergence estimates for an Euler implicit, mixed finite element discretization of Richards' equation, SIAM Journal on Numerical Analysis, 42 (2004), 1452-1478.doi: 10.1137/S0036142902405229.

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