D. Amadori, L. Gosse, and G. Guerra, Godunov-type approximation for a general resonant balance law with large data, Journal of Differential Equations, vol.198, issue.2, pp.233-274, 2004.
DOI : 10.1016/j.jde.2003.10.004

P. [. Andreianov, N. Goatin, and . Seguin, Finite volume schemes for locally constrained conservation laws, Numerische Mathematik, vol.73, issue.115, pp.609-645, 2010.
DOI : 10.1007/s00211-009-0286-7

URL : https://hal.archives-ouvertes.fr/hal-00387806

K. [. Andreianov, N. H. Karlsen, and . Risebro, On vanishing viscosity approximation of conservation laws with discontinuous flux, Netw. Heterog. Media, vol.5, issue.3, pp.617-633, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00438203

K. [. Andreianov, N. H. Karlsen, and . Risebro, A Theory of L 1-Dissipative Solvers for Scalar Conservation Laws with Discontinuous Flux, Archive for Rational Mechanics and Analysis, vol.2, issue.2, 2011.
DOI : 10.1007/s00205-010-0389-4

URL : https://hal.archives-ouvertes.fr/hal-00475840

F. [. Andreianov, N. Lagoutì-ere, T. Seguin, and . Takahashi, Wellposedness for a one-dimensional fluid-particle interaction model
URL : https://hal.archives-ouvertes.fr/hal-00789315

F. [. Andreianov, N. Lagoutì-ere, T. Seguin, and . Takahashi, Small solids in an inviscid fluid, Networks Het. Media, vol.5, issue.3, pp.385-404, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00590617

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

B. [. Audusse and . Perthame, Uniqueness for scalar conservation laws with discontinuous flux via adapted entropies, Proc. Roy. Soc. Edinburgh Sect. A, vol.135, issue.2, pp.253-265, 2005.

]. F. Bac05 and . Bachmann, ´ Equations hyperboliques scalairesàscalaires`scalairesà flux discontinu, 2005.

B. Boutin, F. Coquel, and E. Godlewski, Dafermos Regularization for Interface Coupling of Conservation Laws, Hyperbolic problems: theory, numerics, applications, pp.567-575, 2008.
DOI : 10.1007/978-3-540-75712-2_55

A. [. Bürger, K. H. García, J. D. Karlsen, and . Towers, A family of numerical schemes for kinematic flows with discontinuous flux, Journal of Engineering Mathematics, vol.135, issue.165, pp.3-4387, 2008.
DOI : 10.1007/s10665-007-9148-4

H. [. Baiti and . Jenssen, Well-Posedness for a Class of 2??2 Conservation Laws withL???Data, Journal of Differential Equations, vol.140, issue.1, pp.161-185, 1997.
DOI : 10.1006/jdeq.1997.3308

R. Bürger, K. H. Karlsen, and J. D. Towers, An Engquist???Osher-Type Scheme for Conservation Laws with Discontinuous Flux Adapted to Flux Connections, SIAM Journal on Numerical Analysis, vol.47, issue.3, pp.1684-1712, 2006.
DOI : 10.1137/07069314X

B. [. Botchorishvili, A. Perthame, and . Vasseur, Equilibrium schemes for scalar conservation laws with stiff sources, Mathematics of Computation, vol.72, issue.241, pp.131-157, 2003.
DOI : 10.1090/S0025-5718-01-01371-0

A. [. Chinnayya, N. Leroux, and . Seguin, A well-balanced numerical scheme for the approximation of the shallow-water equations with topography: the resonance phenomenon, Int. J. Finite Volumes, pp.1-33, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00017378

L. [. Crandall and . Tartar, Some relations between nonexpansive and order preserving mappings, Proc. AMS, pp.385-390, 1980.
DOI : 10.1090/S0002-9939-1980-0553381-X

R. Eymard, T. Gallouët, and R. Herbin, Finite volume methods, VII, Handb. Numer. Anal., VII, pp.713-1020, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00346077

]. L. Gl96a, A. Gosse, and . Leroux, Un schéma-´ equilibre adapté aux lois de conservation scalaires non-homogènes, C. R. Acad. Sci. Paris Sér. I Math, vol.323, issue.5, pp.543-546, 1996.

]. J. Gl96b, A. Greenberg, and . Leroux, A well-balanced scheme for the numerical processing of source terms in hyperbolic equations

P. [. Goatin and . Lefloch, The Riemann problem for a class of resonant hyperbolic systems of balance laws, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.21, issue.6, pp.881-902, 2004.
DOI : 10.1016/j.anihpc.2004.02.002

P. [. Godlewski and . Raviart, Hyperbolic systems of conservation laws, of Mathématiques & Applications (Paris) [Mathematics and Applications]. Ellipses, 1991.
URL : https://hal.archives-ouvertes.fr/hal-00113734

]. G. Gue04 and . Guerra, Well-posedness for a scalar conservation law with singular nonconservative source, J. Differential Equations, vol.206, issue.2, pp.438-469, 2004.

B. [. Isaacson and . Temple, Convergence of the $2 \times 2$ Godunov Method for a General Resonant Nonlinear Balance Law, SIAM Journal on Applied Mathematics, vol.55, issue.3
DOI : 10.1137/S0036139992240711

]. S. Kru70 and . Kruzhkov, First order quasilinear equations with several independent variables, Mat. Sb, issue.123, pp.81228-255, 1970.

A. Leroux, Riemann Solvers for some Hyperbolic Problems with a Source Term, Actes du 30ème Congrès d'Analyse Numérique: CANum '98, pp.75-90, 1998.
DOI : 10.1051/proc:1999047

N. [. Lagoutì-ere, T. Seguin, and . Takahashi, A simple 1D model of inviscid fluid-solid interaction, J. Differential Equations, issue.11, pp.2453503-3544, 2008.

]. E. Pan07, . Yu, and . Panov, Existence of strong traces for quasi-solutions of multidimensional conservation laws, J. Hyperbolic Differ. Equ, vol.4, issue.4, pp.729-770, 2007.

J. [. Seguin and . Vovelle, ANALYSIS AND APPROXIMATION OF A SCALAR CONSERVATION LAW WITH A FLUX FUNCTION WITH DISCONTINUOUS COEFFICIENTS, Mathematical Models and Methods in Applied Sciences, vol.13, issue.02, pp.221-257, 2003.
DOI : 10.1142/S0218202503002477

URL : https://hal.archives-ouvertes.fr/hal-01376535

]. A. Vas01 and . Vasseur, Strong traces for solutions of multidimensional scalar conservation laws [Vas02] A. Vasseur. Well-posedness of scalar conservation laws with singular sources, Arch. Ration. Mech. Anal. Methods Appl. Anal, vol.160, issue.92, pp.181-193291, 2001.

]. J. Vov02 and . Vovelle, Convergence of finite volume monotone schemes for scalar conservation laws on bounded domains, Numer. Math, vol.90, issue.3, pp.563-596, 2002.