D. Amadori and L. Gosse, Error estimates for well-balanced schemes on simple balance laws, SpringerBriefs in Mathematics. Springer, Cham; BCAM Basque Center for Applied Mathematics, 2015.
DOI : 10.1007/978-3-319-24785-4

B. Andreianov, K. H. Karlsen, and N. H. 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, pp.27-86, 2011.
DOI : 10.1070/SM1967v002n02ABEH002340
URL : https://hal.archives-ouvertes.fr/hal-00475840

B. Andreianov and N. Seguin, Analysis of a Burgers equation with singular resonant source term and convergence of well-balanced schemes, Discrete Contin. Dyn. Syst, vol.32, issue.6, pp.1939-1964, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00576959

C. Berthon and C. Chalons, A fully well-balanced, positive and entropy-satisfying Godunov-type method for the shallow-water equations, Mathematics of Computation, vol.85, issue.299, pp.1281-1307, 2016.
DOI : 10.1090/mcom3045
URL : https://hal.archives-ouvertes.fr/hal-00956799

F. Bouchut, Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources, Frontiers in Mathematics, 2004.

Y. Brenier, C. De-lellis, L. Székelyhidi, and J. , Weak-Strong Uniqueness for Measure-Valued Solutions, Communications in Mathematical Physics, vol.50, issue.12, pp.351-361, 2011.
DOI : 10.1002/(SICI)1097-0312(199712)50:12<1261::AID-CPA3>3.0.CO;2-6
URL : http://arxiv.org/abs/0912.1028

C. Cancès, H. Mathis, and N. Seguin, Error estimate for time-explicit finite volume approximation of strong solutions to systems of conservation laws

P. Cargo and A. Leroux, Un schémá equilibre adapté au modèle d'atmosphère avec termes de gravité, C. R. Acad. Sci. Paris Sér. I Math, vol.318, issue.1, pp.73-76, 1994.

C. Chalons and F. Coquel, A new comment on the computation of non-conservative products using Roe-type path conservative schemes, Journal of Computational Physics, vol.335, pp.592-604, 2017.
DOI : 10.1016/j.jcp.2017.01.016
URL : https://hal.archives-ouvertes.fr/hal-01424306

C. Chalons, F. Coquel, E. Godlewski, P. Raviart, and N. Seguin, GODUNOV-TYPE SCHEMES FOR HYPERBOLIC SYSTEMS WITH PARAMETER-DEPENDENT SOURCE: THE CASE OF EULER SYSTEM WITH FRICTION, Mathematical Models and Methods in Applied Sciences, vol.323, issue.11, pp.2109-2166, 2010.
DOI : 10.1016/0022-0396(87)90188-4
URL : https://hal.archives-ouvertes.fr/hal-00401616

A. Chinnayya, A. Leroux, and N. 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

J. Colombeau, Multiplication of distributions, 1992.

F. Coquel, K. Saleh, and N. Seguin, A robust and entropy-satisfying numerical scheme for fluid flows in discontinuous nozzles, Mathematical Models and Methods in Applied Sciences, vol.10, issue.10, pp.2043-2083, 2014.
DOI : 10.1016/j.jcp.2013.01.050
URL : https://hal.archives-ouvertes.fr/hal-00795446

C. M. Dafermos, The second law of thermodynamics and stability, Archive for Rational Mechanics and Analysis, vol.70, issue.2, pp.167-179, 1979.
DOI : 10.1007/BF00250353

C. M. Dafermos, Hyperbolic conservation laws in continuum physics, 2010.
DOI : 10.1007/978-3-662-49451-6

G. Dal-maso, P. G. Lefloch, and F. Murat, Definition and weak stability of non conservative products, J. Math. Pures Appl, vol.74, pp.483-548, 1995.

R. J. Diperna, Entropy and the Uniqueness of Solutions to Hyperbolic Conservation Laws, Indiana U. Math. J, vol.28, pp.137-188, 1979.
DOI : 10.1016/B978-0-12-195250-1.50005-9

U. S. Fjordholm, S. Mishra, and E. Tadmor, Well-balanced and energy stable schemes for the shallow water equations with discontinuous topography, Journal of Computational Physics, vol.230, issue.14, pp.5587-5609, 2011.
DOI : 10.1016/j.jcp.2011.03.042

G. Gallice, Solveurs simples positifs et entropiques pour les syst??mes hyperboliques avec terme source, Comptes Rendus Mathematique, vol.334, issue.8, pp.713-716, 2002.
DOI : 10.1016/S1631-073X(02)02307-5

J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Communications on Pure and Applied Mathematics, vol.12, issue.4, pp.697-715, 1965.
DOI : 10.1002/cpa.3160180408

J. Glimm and P. D. Lax, Decay of solutions of systems of nonlinear hyperbolic conservation laws. Memoirs of the, 1970.

P. Goatin and P. G. 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

E. Godlewski and P. Raviart, Numerical approximation of hyperbolic systems of conservation laws, Applied Mathematical Sciences, vol.118, 1996.
DOI : 10.1007/978-1-4612-0713-9

S. K. Godunov, Finite difference method for numerical computation of discontinous solution of the equations of fluid dynamics, Mat. Sb, vol.47, pp.271-300, 1959.

L. Gosse, A WELL-BALANCED SCHEME USING NON-CONSERVATIVE PRODUCTS DESIGNED FOR HYPERBOLIC SYSTEMS OF CONSERVATION LAWS WITH SOURCE TERMS, Mathematical Models and Methods in Applied Sciences, vol.5, issue.02, pp.339-365, 2001.
DOI : 10.2514/3.51181

L. Gosse, Localization effects and measure source terms in numerical schemes for balance laws, Mathematics of Computation, vol.71, issue.238, pp.553-582, 2002.
DOI : 10.1090/S0025-5718-01-01354-0
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.192.3612

L. Gosse, Computing qualitatively correct approximations of balance laws Exponential-fit, well-balanced and asymptotic-preserving
DOI : 10.1007/978-88-470-2892-0

J. M. Greenberg and A. Leroux, A Well-Balanced Scheme for the Numerical Processing of Source Terms in Hyperbolic Equations, SIAM Journal on Numerical Analysis, vol.33, issue.1, pp.1-16, 1996.
DOI : 10.1137/0733001

A. Harten, P. D. Lax, and B. Van-leer, On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws, SIAM Review, vol.25, issue.1, pp.35-61, 1983.
DOI : 10.1137/1025002

E. Isaacson and B. Temple, Nonlinear Resonance in Systems of Conservation Laws, SIAM Journal on Applied Mathematics, vol.52, issue.5, pp.1260-1278, 1992.
DOI : 10.1137/0152073

E. Isaacson and B. 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, pp.625-640, 1995.
DOI : 10.1137/S0036139992240711

V. Jovanovi´cjovanovi´c and C. Rohde, Error Estimates for Finite Volume Approximations of Classical Solutions for Nonlinear Systems of Hyperbolic Balance Laws, SIAM Journal on Numerical Analysis, vol.43, issue.6, pp.2423-2449, 2006.
DOI : 10.1137/S0036142903438136

M. Kang and A. F. Vasseur, Criteria on Contractions for Entropic Discontinuities of Systems of Conservation Laws, Archive for Rational Mechanics and Analysis, vol.22, issue.1, pp.343-391, 2016.
DOI : 10.1007/BF00400379

C. Klingenberg and N. H. Risebro, Convex conservation laws with discontinuous coefficients. existence, uniqueness and asymptotic behavior, Communications in Partial Differential Equations, vol.22, issue.11-12, pp.11-121959, 1995.
DOI : 10.1137/0522059

B. Perthame and C. Simeoni, A kinetic scheme for the Saint-Venant system??with a source term, Calcolo, vol.38, issue.4, pp.201-231, 2001.
DOI : 10.1007/s10092-001-8181-3
URL : https://hal.archives-ouvertes.fr/hal-00922664

E. Tadmor, The numerical viscosity of entropy stable schemes for systems of conservation laws. I, Mathematics of Computation, vol.49, issue.179, pp.91-103, 1987.
DOI : 10.1090/S0025-5718-1987-0890255-3

B. Temple and R. Young, A Nash???Moser Framework for Finding Periodic Solutions of the Compressible Euler Equations, Journal of Scientific Computing, vol.46, issue.1, pp.761-772, 2015.
DOI : 10.1002/cpa.3160460605

E. F. Toro, Riemann solvers and numerical methods for fluid dynamics
DOI : 10.1007/978-3-662-03915-1