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

B. Andreianov and F. Bouhsiss, Uniqueness for an elliptic-parabolic problem with Neumann boundary condition, J. Evol. Equ, vol.4, pp.273-295, 2004.

B. Andreianov and N. Igbida, On uniqueness techniques for degenerate convection-diffusion problems, International Journal of Dynamical Systems and Differential Equations, vol.4, issue.1/2, pp.4-112
DOI : 10.1504/IJDSDE.2012.045992

URL : https://hal.archives-ouvertes.fr/hal-00553819

B. Andreianov and K. Shibi, Scalar conservation laws with nonlinear boundary conditions, Comptes Rendus Mathematique, vol.345, issue.8, pp.431-434, 2007.
DOI : 10.1016/j.crma.2007.09.008

URL : https://hal.archives-ouvertes.fr/hal-00475852

C. Bardos, A. Y. Le-roux, and J. C. Nedelec, First order quasilinear equations with boundary conditions, Communications in Partial Differential Equations, vol.2, issue.33, pp.1017-1034, 1979.
DOI : 10.1090/S0025-5718-1977-0478651-3

. Ph, . Bénilan, M. G. Crandall, and A. Pazy, Nonlinear evolution equations in Banach spaces

. Ph and H. Bénilan, Toure, Sur l'´ equation générale ut = a(., u, ?(., u)x)x + v dans L 1 . I. Etude du probleme stationnaire, Evolution equations (Baton Rouge, p.35, 1992.

. Ph, P. Bénilan, and . Wittbold, On mild and weak solutions of elliptic-parabolic problems, Adv. Differential Equations, vol.1, issue.6, pp.1053-1073, 1996.

H. Brezis, Functional Analysis, Sobolev Space and Partial Differential Equation, 2010.
DOI : 10.1007/978-0-387-70914-7

R. Bürger, H. Frid, and K. H. Karlsen, On the well-posedness of entropy solutions to conservation laws with a zero-flux boundary condition, Journal of Mathematical Analysis and Applications, vol.326, issue.1, pp.108-120, 2007.
DOI : 10.1016/j.jmaa.2006.02.072

R. Bürger, H. Frid, and K. H. Karlsen, On a free boundary problem for a strongly degenerate quasilinear parabolic equation with an application to a model of presssure filtration, SIAM J. Math. Anal, pp.34-611, 2003.

C. Cancés and T. Gallouët, On the time continuity of entropy solutions, Journal of Evolution Equations, vol.2, issue.4, pp.43-45, 2011.
DOI : 10.1007/s00028-010-0080-0

J. Carrillo, Entropy Solutions for Nonlinear Degenerate Problems, Archive for Rational Mechanics and Analysis, vol.147, issue.4, pp.269-361, 1999.
DOI : 10.1007/s002050050152

G. Gagneux and M. Madaune-tort, Analyse mathématique de modeles nonlinéaires de l'ingégnerie pétroliere, Mathématique et Applications, vol.22, 1996.

S. N. Kruzkhov, FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES, Mathematics of the USSR-Sbornik, vol.10, issue.2, pp.217-243, 1970.
DOI : 10.1070/SM1970v010n02ABEH002156

C. Mascia, A. Porretta, and A. Terracina, Nonhomogeneous Dirichlet Problems for Degenerate Parabolic-Hyperbolic Equations, Archive for Rational Mechanics and Analysis, vol.163, issue.2, pp.87-124, 2002.
DOI : 10.1007/s002050200184

URL : https://hal.archives-ouvertes.fr/hal-00903328

M. Marcus and V. J. , Absolute continuity on tracks and mappings of Sobolev spaces, Archive for Rational Mechanics and Analysis, vol.45, issue.4, pp.294-320, 1972.
DOI : 10.1007/BF00251378

A. Michel and J. Vovelle, Entropy Formulation for Parabolic Degenerate Equations with General Dirichlet Boundary Conditions and Application to the Convergence of FV Methods, SIAM Journal on Numerical Analysis, vol.41, issue.6, pp.41-2262, 2003.
DOI : 10.1137/S0036142902406612

URL : https://hal.archives-ouvertes.fr/hal-01376539

E. Yu and . Panov, On the strong pre-compactness property for entropy solutions of a degenerate elliptic equation with discontinuous flux, J. Differential Equations, vol.247, p.28212870, 2009.

E. Rouvre and G. Gagneux, Formulation forte entropique de lois scalaires hyperboliques-paraboliques dgnres, An. Fac. Sci. Toulouse. X, issue.1, pp.163-183, 2001.

G. Vallet, Dirichlet problem for a degenerated hyperbolic-parabolic equation, Advance in Math. Sci. Appl, vol.15, issue.2, 2005.

A. Vasseur, Strong Traces for Solutions of Multidimensional Scalar Conservation Laws, Archive for Rational Mechanics and Analysis, vol.160, issue.3, pp.181-193, 2001.
DOI : 10.1007/s002050100157

B. Andreianov-laboratoire-de-mathématiques and C. , UMR 6623 -Université de Franche-Comte 16, route de Gray 25030 Besancon France e-mail: boris.andreianov@univ-fcomte, fr Mohamed Karimou Gazibo Laboratoire de Mathématiques CNRS : UMR 6623 -Université de Franche-Comte 16