G. Allaire and X. Bec, -Schéma d'ordre 2 en temps pour le code FLICA-4 -Note interne CEA DMT 96, p.395, 1943.
URL : https://hal.archives-ouvertes.fr/hal-01258747

C. Bardos, Introduction auxprobì emes hyperboliques non-linéaires -Lecture notes in math, pp.2-74

C. Bardos, A. Y. Leroux, and J. C. Nedelec, -First order quasilinear equations with boundary conditions -Comm. part. diff, p.1017, 1034.
DOI : 10.1080/03605307908820117

URL : https://hal.archives-ouvertes.fr/hal-00019803

M. Ben-artzi and J. Falconvitz, -An upwind 2nd order scheme for compressible duct flows -SIAM, J. of Sci. Stat. Comp, vol.7, issue.3, pp.744-768, 1986.
URL : https://hal.archives-ouvertes.fr/hal-01283671

F. Bereux, E. Bonnetier, and P. Lefloch, -Gas dynamics system: two special cases -Rapport interne CMAP No 325, 1995.

F. Bereux and L. Sainsaulieu, Roe-type Riemann solver for hyperbolic systems with relaxation based on time-dependant wave decomposition -Mémoire d'habilitationàhabilitationà diriger des recherches, 1995.

M. Blunt and B. Rubin, -Implicit flux limiting schemes for petroleum reservoir simulation, pp.102-194, 1992.
URL : https://hal.archives-ouvertes.fr/in2p3-00000011

P. Cargo and A. Y. Leroux, -Un schémá equilibre adapté au modèle d'atmosphère avec termes de gravité -C.R. Acad. Sc. Série A t, p.31876, 1994.
URL : https://hal.archives-ouvertes.fr/hal-00250203

J. J. Cauret, J. F. Colombeau, and A. Y. Leroux, -Discontinuous generalized solutions of nonlinear nonconservative hyperbolic equations, J. Math. Anal. Applic, pp.139-552, 1989.
URL : https://hal.archives-ouvertes.fr/hal-00587793

G. Q. Chen and J. Glimm, -Global solutions to the compressible Euler equations with geometrical structure - Comm, Math. Phys. vol, vol.180, pp.1-159, 1996.
URL : https://hal.archives-ouvertes.fr/hal-00109057

G. Q. Chen, C. D. Levermore, and T. P. Liu, -Hyperbolic conservation laws with stiff relaxation terms and entropy -Comm, Pure and Applied Math, vol.47, issue.787, p.830, 1994.
URL : https://hal.archives-ouvertes.fr/hal-00109057

G. Q. Chen and T. P. Liu, -Zero relaxation and dissipation limits for hyperbolic systems of conservation laws - Comm, Pure and Applied Math, vol.46, pp.755-781, 1993.
URL : https://hal.archives-ouvertes.fr/hal-00109057

P. G. Ciarlet, -IntroductionàIntroductionà l'analyse numérique matricielle etàetà l'optimisation -Maitrise de mathématiques Masson, 1980.
URL : https://hal.archives-ouvertes.fr/inria-00073463

S. Clerc, Décomposition de domaine pour un système hyperbolique: applications aux schémas implicites en mécanique des fluides -Note interne CEA DMT 96, p.284, 1915.

S. Clerc, Etude de schémas décentrés implicites pour le calcul numérique en mécanique des fluides. Résolution par décomposition de domaines -Thèse de l'université Paris VI -1997

B. Dacorogna, Weak continuity and weak lower-continuity of non-linear functionnals -Lecture notes in math, p.922

D. Maso, G. Lefloch, P. Murat, and F. , -Definition and weak stability of a non-conservative product, J. Math. Pures et Appliquées, vol.74, issue.6, pp.483-548, 1995.
URL : https://hal.archives-ouvertes.fr/hal-00555215

A. J. Desanti, -Boundary and interior layer behavior of solutions of some singularly perturbed semilinear elliptic boundary value problems, J. Math. pures et appliquées, vol.65, issue.423, p.468, 1986.
URL : https://hal.archives-ouvertes.fr/pasteur-00336957

R. A. Devore and B. J. Lucier, -On the size and smoothness of solutions to nonlinear hyperbolic conservation laws -SIAM, J. of Math. Anal, vol.27, issue.3, pp.684-707, 1996.
URL : https://hal.archives-ouvertes.fr/hal-00137881

F. Devuyst, Schémas non-conservatifs et cinétiques pour la simulation numérique d'´ ecoulements hypersoniques non-visqueux en déséquilibre thermochimique -Thèse de doctorat de l, 1994.

R. Diperna, Convergence of approximate solutions to conservation laws -Arch. rational mech. and anal, pp.27-70, 1983.

R. Diperna, Measure-valued solutions to conservation laws -Arch. rational mech. and anal, pp.223-270, 1985.

F. Dubois, Conditions aux limites fortement non-linéaires pour leséquationsleséquations d'Euler -Ecole CEA, EDF, INRIA sur lesprobì emes non-linéaires appliqués (P.L. Lions org, pp.9-11, 1988.

F. Dubois and P. Lefloch, -Boundary conditions for nonlinear hyperbolic systems of conservation laws -J. of Diff. Eqs, pp.93-122, 1988.
URL : https://hal.archives-ouvertes.fr/halshs-00607616

E. Weinan and -. , Homogeneization of scalar conservation laws with oscillatory forcing terms -SIAM, J. of Appl. Math, vol.52, pp.4-959, 1992.

P. Embid, J. Goodman, and A. Majda, -Multiple steady-states for 1D transonic flow -SIAM, J. of Sci. Stat. Comp. Vol, vol.5, issue.1, pp.21-41, 1984.
URL : https://hal.archives-ouvertes.fr/in2p3-00656399

H. Fan and J. Hale, -Large-time behavior in inhomogeneous conservation laws -Arch. rational mech. and anal, p.216, 1993.
URL : https://hal.archives-ouvertes.fr/hal-00358066

P. Glaister, -Flux difference splitting for hyperbolic systems of conservation laws with source terms -Comp, Math. Applic. vol, vol.26, pp.7-79, 1993.

H. M. Glaz and T. P. Liu, The asymptotic analysis of wave interactions and numerical calculations of transonic nozzle flows -Adv. in Applied Math, pp.111-146, 1984.

J. Glimm and G. Marshall, Plohr -A generalized Riemann problem for quasi one dimensional gas flows -Adv. in Applied Math, pp.1-30, 1984.

E. Godlewski and P. A. Raviart, -Hyperbolic systems of conservation laws (Ellipses-SMAI, 1991.
URL : https://hal.archives-ouvertes.fr/hal-00958679

S. K. Godunov, -Finite difference schemes for numerical computation of solutions of the equations of fluid dynamics -Math, USSR Sbornik -Vol, vol.47, issue.271, p.306, 1959.
URL : https://hal.archives-ouvertes.fr/inria-00074377

L. Gosse, Systèmes hyperboliques non homogènes: introduction de solveurs de Riemann ¡¡équilibre¿¿ - Note interne CEA DMT 96, p.260, 1908.

L. Gosse, -Stabilité des méthodes de Runge-Kutta pour les EDP hyperboliques non-homogènes -Note interne CEA DMT 96, p.525, 1973.
URL : https://hal.archives-ouvertes.fr/halshs-00706743

L. Gosse and A. Y. Leroux, -Un schéma-´ equilibre adapté aux lois de conservation scalaires non-homogènes - C.R. Acad. Sc. Série A -t, pp.323-543, 1996.
DOI : 10.1016/s0764-4442(99)80466-2

URL : https://hal.archives-ouvertes.fr/halshs-00706743

J. Greenberg and A. Y. Leroux, -A well balanced scheme for the numerical processing of source terms in hyperbolic equations -SIAM J. Numer. Anal, pp.1-16, 1996.
URL : https://hal.archives-ouvertes.fr/inria-00510145

J. Greenberg, A. Y. Leroux, R. Baraille, and A. Noussair, -Analyse et approximations de lois de conservation avec terme source -C.R. Acad. Sc. Série A -t, pp.321-1073, 1995.
URL : https://hal.archives-ouvertes.fr/inria-00510145

E. Hairer, S. P. Norsett, and G. Wanner, -Solving ordinary differential equations I nonstiff problems -Springer series in computationnal mathematics
URL : https://hal.archives-ouvertes.fr/hal-00732063

E. Hairer and G. Wanner, -Solving ordinary differential equations II stiff problems -Springer series in computationnal mathematics, p.14
URL : https://hal.archives-ouvertes.fr/hal-00732063

A. Heibig and J. F. Colombeau, -Non-conservative products in bounded variation functions -SIAM, J. Math. Anal, vol.23, pp.4-941, 1992.
URL : https://hal.archives-ouvertes.fr/hal-00869160

H. Holgen, N. Risebro, and A. Tveito, -Maximum principles for a class of conservation laws -SIAM, J. of Appl. Math, vol.55, pp.3-651, 1995.

L. Hsiao and T. P. Liu, -Convergence to nonlinear diffusion waves for solutions of a system of hyperbolic conservation laws with damping -Comm, Math. Phys, vol.143, pp.599-605, 1992.
URL : https://hal.archives-ouvertes.fr/in2p3-00186269

E. Isaacson and B. Temple, -Nonlinear resonance for systems of conservation laws, SIAM J. Appl. Math, vol.52, issue.5, pp.1260-1278, 1992.
URL : https://hal.archives-ouvertes.fr/hal-00589432

E. Isaacson and B. Temple, -Convergence of the 2x2 Godunov method for a general resonant nonlinear balance law, SIAM J. Appl. Math, vol.55, issue.3, pp.625-640, 1995.
URL : https://hal.archives-ouvertes.fr/hal-00589432

J. S. Levermore and C. D. , -Numerical schemes for hyperbolic conservation laws with stiff relaxation terms, J.C.P. No, vol.126, pp.449-467, 1996.
URL : https://hal.archives-ouvertes.fr/hal-00020758

J. S. Liu and J. G. , -The effects of numerical viscosities (I) Slowly moving shocks, J.C.P. No, vol.126, pp.373-389, 1996.
URL : https://hal.archives-ouvertes.fr/tel-00259428

S. N. Kruzkov, -First order quasilinear equations in several independant space variables -Math, USSR Sbornik -No, vol.10, issue.217, p.243, 1970.

B. Larroutourou, -How to preserve the mass fractions positivity when computing multi-component flows, J.C.P. vol, vol.95, pp.59-84, 1991.

B. Larroutourou and L. Fezoui, On the equations of multi-component perfect or real gas inviscid flow -in ¡¡Nonlinear hyperbolic problems¿¿ Lecture notes in math, 1989.

P. Lascaux and R. Théodor, Analyse matricielle appliquéè a l'art de l'ingénieur I Méthodes directes, p.-Masson, 1993.

P. D. Lax, Hyperbolic systems of conservation laws and the mathematical theory of shock waves -Conference Board, Mathematical Sciences / National Science Foundation, vol.11

P. Lax and B. Wendroff, -Systems of conservation laws -Comm. Pure and Applied Math, pp.7-159, 1954.
URL : https://hal.archives-ouvertes.fr/in2p3-00025911

A. Lerat, -Implicit time dependant methods for the solution of the Euler equations (Lecture 04 -VonKarman Institute, 1984.
URL : https://hal.archives-ouvertes.fr/hal-01207239

R. J. Leveque, -Numerical methods for conservation laws: stiff source terms (Lecture 04 -VonKarman Institute, 1988.
URL : https://hal.archives-ouvertes.fr/hal-00807582

P. L. Lions, B. Perthame, and E. Tadmor, -Formulation cinétique de lois de conservation scalaires multidimensionnelles -C.R. Acad. Sc. Série A -t, pp.312-97, 1991.
URL : https://hal.archives-ouvertes.fr/hal-01058658

L. Ta-tsien, -Global classical solutions for hyperbolic systems (Coll. RMA 24 -Masson, 1994.

T. P. Liu, -Hyperbolic conservation laws with relaxation -Comm, Math. Phys, vol.108, pp.153-175, 1987.
URL : https://hal.archives-ouvertes.fr/tel-00259428

C. Mascia, -Travelling wave solutions for a balance law -Preprint, 1996.
URL : https://hal.archives-ouvertes.fr/hal-00512508

F. Murat, -A survey on compensated compactness, in Contributions to modern calculus of variations -L
URL : https://hal.archives-ouvertes.fr/halshs-00260352

C. Eds, Research notes in math. (No 148 pp145, pp.183-1987

F. Otto, -Initial-boundary value problem for a scalar conservation law -C, .R. Acad. Sc. t.322 Série I, pp.729-734, 1996.
URL : https://hal.archives-ouvertes.fr/in2p3-00025581

B. Perthame and C. W. Shu, -On positivity preserving finite volume schemes for the Euler equations -Num, Math, pp.73-119, 1996.
URL : https://hal.archives-ouvertes.fr/hal-00859393

J. L. Richardson and R. C. Ferrell, -Unconditionally stable explicit algorithms for nonlinear fluid dynamics problems, J.C.P, vol.104, pp.69-74, 1993.
URL : https://hal.archives-ouvertes.fr/jpa-00209836

P. L. Roe, -Approximate Riemann solvers, parameter vectors, and difference schemes, pp.43-357, 1981.
DOI : 10.1016/0021-9991(81)90128-5

URL : https://hal.archives-ouvertes.fr/in2p3-00025581

H. H. Rosenbrock, -Some general implicit processes for the numerical solutions of differential equations - Comput, J, pp.5-329, 1963.

D. Serre, Systèmes de lois de conservation -Coll, Fondations Diderot, 1996.

C. W. Shu, -A numerical method for systems of conservation laws of mixed type admitting hyperbolic flux splitting, J.C.P, vol.100, pp.424-429, 1992.
URL : https://hal.archives-ouvertes.fr/hal-00908981

C. W. Shu, Osher S. -Efficient implementation of essentially non-oscillatory shock-capturing schemes, pp.77-439, 1988.

J. Smoller, -Shock waves and reaction-diffusion equations (258, 1982.
URL : https://hal.archives-ouvertes.fr/hal-01246688

L. Tartar, Compensated compactness and aplications to partial differential equations, in Nonlinear analysis and mechanics: Heriot-Watt symposium vol, J. Knops Eds. Research notes in math, vol.4, 1979.

I. Toumi, Schémas de type Godunov pour lesécoulementslesécoulements diphasiques multidimensionnels -Thèse de doctorat de l'Université Paris VI -1989

I. Toumi, -A weak formulation of Roe's aproximate Riemann, pp.2-360, 1992.
URL : https://hal.archives-ouvertes.fr/hal-01133271

B. Vanleer, -Flux-vector splitting for the Euler equations -Lectures Notes in Physics -vol, pp.507-512, 1982.
URL : https://hal.archives-ouvertes.fr/hal-00315124

B. Vanleer, On the relation between the upwind differencing schemes of Engquist-Oscher, Godunov and Roe -SIAM, J. of Sci. Stat. Comp. Vol, vol.5, issue.1, pp.1-20, 1984.

D. H. Wagner, -The transformation from Eulerian to Lagrangian coordinates for solutions with discontinuities -Nonlinear hyperbolic problems Proceedings St Etienne, 1986.
URL : https://hal.archives-ouvertes.fr/hal-00857449

H. C. Yee, R. M. Beam, and R. F. Warming, -Boundary approximations for implicit schemes for one-dimensional inviscid equations of gas dynamics, AIAA Journal, vol.20, pp.9-1203, 1982.
URL : https://hal.archives-ouvertes.fr/in2p3-01010168

H. C. Yee, P. K. Sweby, and D. F. Griffiths, -Dynamical approach study of spurious steady-state numerical solutions for nonlinear differential equations, Part I: the dynamics of time discretizations and its implications for algorithm development in computational fluid dynamics, p.97310, 1991.
URL : https://hal.archives-ouvertes.fr/in2p3-01010168

A. Zelmanse, -Formulation cinétique et schémas de Boltzmann pour le calcul numérique en mécanique des fluides -Thèse de doctorat de l'Université Paris XIII -1994

X. Zhong, Additive semi-implicit Runge-Kutta methods for computing high-speed non equilibrium reactive flows, pp.128-147, 1996.