| Publication type: |
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Preprint, Working Paper, ... |
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| Subject: |
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Mathematics/Analysis of PDEs
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| Title: |
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On Intrinsic Formulation and Well-posedness of a Singular Limit of Two-phase Flow Equations in Porous Media |
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| Author(s): |
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Boris Andreianov ( ) 1, Robert Eymard () 2, Mustapha Ghilani () 3, Nouzha Marhraoui () 3 |
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| Laboratory: |
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| Abstract: |
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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: \begin{equation*} \left\{ \begin{array}{l} u_t - \div(k_w(u) \nabla p)&=& \splus - \theta \smoins \char_{[u=1]}, \\ u=1 &\hbox{or}& \grad(p + \Pc(u)) = 0 \hbox{ a.e. in } \O\times(0,T) \end{array} \right. \end{equation*} was derived in the works \cite{MHenry-et-al} and \cite{AndrEymardGhilaniMarhraoui} (see also \cite{Eymard-Ghilani-Marhraoui}). 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. \cite{PlouvierGagneux,Plouvier,ProuvierEtAl-Cras}. For the no-source case, we justify the equivalence of the Generalized Richards Equation and the classical Richards model. |
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| Fulltext language: |
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English |
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| Production date: |
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2011-04-01 |
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| Keyword(s): |
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Flow in porous medium – two-phase flow model – Richards model – renormalized solutions |
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| Contract, financing: |
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Project PARS MI 06, CNRST and Project 24506 CNRS-CNRST SPM08/10 |
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