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

Boris Andreianov, Robert Eymard, Mustapha Ghilani, Nouzha Marhraoui

• 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.