G. D. Adimurthi, . Veerappa, and . Gowda, Conservation law with discontinuous flux, Journal of Mathematics of Kyoto University, vol.43, issue.1, pp.27-70, 2003.
DOI : 10.1215/kjm/1250283740

J. Adimurthi, G. D. Jaffré, . Veerappa, and . Gowda, Godunov-Type Methods for Conservation Laws with a Flux Function Discontinuous in Space, SIAM Journal on Numerical Analysis, vol.42, issue.1, pp.179-208, 2004.
DOI : 10.1137/S003614290139562X

S. Adimurthi, G. D. Mishra, . Veerappa, and . Gowda, OPTIMAL ENTROPY SOLUTIONS FOR CONSERVATION LAWS WITH DISCONTINUOUS FLUX-FUNCTIONS, Journal of Hyperbolic Differential Equations, vol.02, issue.04, pp.783-837, 2005.
DOI : 10.1142/S0219891605000622

S. Adimurthi, G. D. Mishra, . Veerappa, and . Gowda, Conservation law with the flux function discontinuous in the space variable???II, Journal of Computational and Applied Mathematics, vol.203, issue.2, pp.310-344, 2007.
DOI : 10.1016/j.cam.2006.04.009

S. Adimurthi, G. D. Mishra, . Veerappa, and . Gowda, Existence and stability of entropy solutions for conservation laws with discontinuous non-convex fluxes, Networks and Heterogeneous Media, pp.127-157, 2007.

S. Adimurthi, G. D. Mishra, . Veerappa, and . Gowda, Convergence of Godunov type methods for a conservation law with a spatially varying discontinuous flux function, Mathematics of Computation, vol.76, issue.259, pp.1219-1242, 2007.
DOI : 10.1090/S0025-5718-07-01960-6

K. Aziz and A. Settari, Petroleum Reservoir Simulation, 1979.

R. Burger, K. H. Karlsen, N. H. Risebro, and J. D. Towers, Wellposedness in BV t and convergence of a difference scheme for continuous sedimentation in ideal clarifier thickener units, Numer. Math, pp.97-122, 2004.

Y. Brenier and J. Jaffré, Upstream Differencing for Multiphase Flow in Reservoir Simulation, SIAM Journal on Numerical Analysis, vol.28, issue.3, pp.685-696, 1991.
DOI : 10.1137/0728036

URL : https://hal.archives-ouvertes.fr/inria-00075414

G. M. Coclite and N. H. Risebro, Conservation Laws with Time Dependent Discontinuous Coefficients, SIAM Journal on Mathematical Analysis, vol.36, issue.4, pp.1293-1309, 2005.
DOI : 10.1137/S0036141002420005

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.229.813

M. G. Crandall and A. Majda, Monotone difference approximations for scalar conservation laws, Mathematics of Computation, vol.34, issue.149, pp.1-2, 1980.
DOI : 10.1090/S0025-5718-1980-0551288-3

S. Diehl, On Scalar Conservation Laws with Point Source and Discontinuous Flux Function, SIAM Journal on Mathematical Analysis, vol.26, issue.6, pp.1425-1451, 1995.
DOI : 10.1137/S0036141093242533

S. Diehl, A conservation Law with Point Source and Discontinuous Flux Function Modelling Continuous Sedimentation, SIAM Journal on Applied Mathematics, vol.56, issue.2, pp.388-419, 1996.
DOI : 10.1137/S0036139994242425

T. Gimse and N. H. Risebro, Riemann problems with discontinuous flux function, Proc. 3rd Internat. Conf. Hyperbolic problems Studentlitteratur, pp.488-502, 1991.

T. Gimse and N. H. Risebro, Solution of the Cauchy Problem for a Conservation Law with a Discontinuous Flux Function, SIAM Journal on Mathematical Analysis, vol.23, issue.3, pp.635-648, 1992.
DOI : 10.1137/0523032

E. Godlewski and P. A. Raviart, Hyperbolic systems of Conservation laws, Mathematiques et Applications, 1991.
URL : https://hal.archives-ouvertes.fr/hal-00113734

S. Godunov, Finite difference methods for numerical computation of discontinuous solutions of the equations of fluid dynamics, Math. Sbornik, pp.47-271, 1959.

K. H. Karlsen, N. H. Risebro, and J. D. Towers, Upwind difference approximations for degenerate parabolic convection-diffusion equations with a discontinuous coefficient, IMA Journal of Numerical Analysis, vol.22, issue.4, pp.623-664, 2002.
DOI : 10.1093/imanum/22.4.623

K. H. Karlsen, N. H. Risebro, and J. D. , Towers, L 1 stability for entropy solution of nonlinear degenerate parabolic convection-diffusion equations with discontinuous coefficients, Skr. K. Nor. Vidensk. Selsk, issue.3, 2003.

J. Jaffré, J. Applications, M. J. Glimm, J. W. Graham, and B. Grove, Numerical calculation of the flux across an interface between two rock types of a porous medium for a two-phase flow, Hyperbolic Problems: Theory, Numerics, pp.165-177, 1996.

E. Kaasschieter, Solving the Buckley-Leverret equation with gravity in a heteregenous porous media, Computational Geosciences, vol.3, issue.1, pp.23-48, 1999.
DOI : 10.1023/A:1011574824970

N. N. Kuznecov and S. A. Volosine, Monotone difference approximations for a first order quasilinear equation, Soviet Math. Dokl, vol.17, pp.1203-1206, 1976.

S. Mochon, An analysis of the traffic on highways with changing surface conditions, Mathematical Modelling, vol.9, issue.1, pp.1-11, 1987.
DOI : 10.1016/0270-0255(87)90068-6

D. A. Ross, Two new moving boundary problems for scalar conservation laws, Communications on Pure and Applied Mathematics, vol.10, issue.5, pp.725-737, 1988.
DOI : 10.1002/cpa.3160410511

P. H. Sammon, An Analysis of Upstream Differencing, SPE Reservoir Engineering, vol.3, issue.03, pp.1053-1056, 1988.
DOI : 10.2118/14045-PA

S. Mishra, Scalar Conservation Laws with Discontinuous flux, Indian Institute of Science, 2003.

S. Mishra, Convergence of Upwind Finite Difference Schemes for a Scalar Conservation Law with Indefinite Discontinuities in the Flux Function, SIAM Journal on Numerical Analysis, vol.43, issue.2, pp.559-577, 2005.
DOI : 10.1137/030602745

B. Temple, Global solution of the cauchy problem for a class of 2 ?? 2 nonstrictly hyperbolic conservation laws, Advances in Applied Mathematics, vol.3, issue.3, pp.335-375, 1982.
DOI : 10.1016/S0196-8858(82)80010-9

J. D. Towers, Convergence of a Difference Scheme for Conservation Laws with a Discontinuous Flux, SIAM Journal on Numerical Analysis, vol.38, issue.2, pp.681-698, 2000.
DOI : 10.1137/S0036142999363668

J. D. Towers, A Difference Scheme for Conservation Laws with a Discontinuous Flux: The Nonconvex Case, SIAM Journal on Numerical Analysis, vol.39, issue.4, pp.1197-1218, 2001.
DOI : 10.1137/S0036142900374974