On Intrinsic Formulation and Well-posedness of a Singular Limit of Two-phase Flow Equations in Porous Media

• Autores: Boris Andreianov, Robert Eymard, Mustapha Ghilani, Nouzha Marhraoui
• Localización: Monografías de la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza, ISSN 1132-6360, Nº. 38, 2012 (Ejemplar dedicado a: Monique Madaune-Tort), págs. 21-34
• Idioma: inglés
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• Resumen

  • Starting from a two-phase flow model in porous media with the viscosity of the “mobile” phase going to infinity, the Generalized Richards Equation for the “viscous” phase:

    ut − div(kw(u)∇p) = s − s1l[u=1], ka(u)∇(p + pc(u)) = 0 a.e. in × (0, T) was derived in the works [6] and [2] (see also [4]). We discuss intrinsic formulations (weak solutions, renormalized solutions) of this singular limit problem, using in particular the techniques developed by Plouvier-Debaigt, Gagneux et al. [13, 11, 12].

    For the no-source case, we justify the equivalence of the Generalized Richards Equation and the classical Richards model.