H. W. Alt and E. D. Benedetto, Nonsteady flow of water and oil through inhomogeneous porous media, Annali della seno la Normale Superiore di Pisa, pp.335-392, 1985.

H. W. Alt and S. Luckhaus, Quasilinear elliptic-parabolic differential equations, Math-Z, vol.183, issue.3, pp.311-341, 1983.

B. Andreianov, M. Bendahmane, and K. H. Karlsen, DISCRETE DUALITY FINITE VOLUME SCHEMES FOR DOUBLY NONLINEAR DEGENERATE HYPERBOLIC-PARABOLIC EQUATIONS, Journal of Hyperbolic Differential Equations, vol.07, issue.01, pp.1-67, 2010.
DOI : 10.1142/S0219891610002062

URL : https://hal.archives-ouvertes.fr/hal-00475752

B. Andreianov, R. Eymard, M. Ghilani, and N. Marhraoui, On intrinsic formulation and well-posedness of a singular limit of two-phase flow equations in porous media, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00606948

B. Andreianov, M. Gutnic, and P. Wittbold, Convergence of Finite Volume Approximations for a Nonlinear Elliptic-Parabolic Problem: A "Continuous" Approach, SIAM Journal on Numerical Analysis, vol.42, issue.1, pp.228-251, 2004.
DOI : 10.1137/S0036142901400006

URL : https://hal.archives-ouvertes.fr/hal-00129680

J. Carrillo, Unicité des solutions du type kruskhov pour desprobì emes elliptiques avec des termes de transport non linéaires, C. R. Acad. Sci. Paris Sér. I Math, vol.303, issue.5, pp.189-192, 1986.

Z. Chen, Degenerate two phase flow incompressible flow 1 : existence, uniqueness and regularity of a weak solution, 1997.

Z. Chen, M. Espedal, and R. Ewing, Continuous time finite element analysis of multiphase flow in groundwater hydrology, Appl. Math, issue.40, pp.203-226, 1995.

Z. Chen and R. Ewing, Mathematical Analysis for Reservoir Models, SIAM Journal on Mathematical Analysis, vol.30, issue.2, pp.431-453, 1999.
DOI : 10.1137/S0036141097319152

K. Deimling, Nonlinear Functional Analysis, 1985.
DOI : 10.1007/978-3-662-00547-7

R. Eymard, T. Gallouët, and R. Herbin, The finite volume methods. The Handbook of Numerical Analysis, 2000.

R. Eymard, T. Gallouët, R. Herbin, and A. Michel, Convergence of a finite volume scheme for nonlinear degenerate parabolic equations, Numerische Mathematik, vol.92, issue.1, pp.41-82, 2002.
DOI : 10.1007/s002110100342

R. Eymard, M. Ghilani, and N. Marhraoui, Convergence of two phase flow to richards model, Finite Volumes for Complex Applications IV. ISTE, 2005.

R. Eymard, M. Henry, and D. Hilhorst, Singular limit of a two-phase flow problem in porous medium as the air viscosity tends to zero, Discrete Cont. Dynamical Syst. S, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00424924

R. Eymard, R. Herbin, and A. Michel, Mathematical study of a petroleum-engineering scheme, ESAIM: Mathematical Modelling and Numerical Analysis, vol.37, issue.6, pp.937-972, 2003.
DOI : 10.1051/m2an:2003062

P. Fabrie and T. Gallouët, Modelling wells in porous media, M3AS Math. Models Meth. Qppl. Sci, vol.10, issue.5, pp.673-709, 2000.

G. Gagneux and M. Madaune-tort, Analyse Mathématique de Modèles non linéaires de l'ingénieriepétrolì ere, Mathématiques & Applications, vol.22, 1996.

D. Kroener and S. Luckhaus, Flow of oil and water in a porous medium, Journal of Differential Equations, vol.55, issue.2, pp.276-288, 1984.
DOI : 10.1016/0022-0396(84)90084-6

A. Michel, Convergence de sch´massch´ sch´mas volumes finis pour desprobì emes de convection diffusion non linéaires, 2001.

A. Michel, A Finite Volume Scheme for Two-Phase Immiscible Flow in Porous Media, SIAM Journal on Numerical Analysis, vol.41, issue.4, pp.1301-1317, 2004.
DOI : 10.1137/S0036142900382739

F. Otto, L1-Contraction and Uniqueness for Quasilinear Elliptic???Parabolic Equations, Journal of Differential Equations, vol.131, issue.1, p.2038, 1996.
DOI : 10.1006/jdeq.1996.0155

A. Plouvier-debaight, Solutions renormalis??es pour des ??quations autonomes des milieux poreux, Annales de la facult?? des sciences de Toulouse Math??matiques, vol.6, issue.4, pp.727-743, 1997.
DOI : 10.5802/afst.886

A. Plouvier-debaight, B. Donné, G. Gagneux, and P. Urruty, Solutions renormalis??es pour des mod??les des milieux poreux, Comptes Rendus de l'Acad??mie des Sciences - Series I - Mathematics, vol.325, issue.10, pp.1091-1095, 1997.
DOI : 10.1016/S0764-4442(97)88711-3

L. A. Richards, CAPILLARY CONDUCTION OF LIQUIDS THROUGH POROUS MEDIUMS, Physics, vol.1, issue.5, pp.318-333, 1931.
DOI : 10.1063/1.1745010