M. R. Baer and J. W. Nunziato, A two-phase mixture theory for the deflagration-to-detonation transition (ddt) in reactive granular materials, International Journal of Multiphase Flow, vol.12, issue.6, pp.861-889, 1986.
DOI : 10.1016/0301-9322(86)90033-9

J. B. Bdzil, R. Menikoff, S. F. Son, A. K. Kapila, and D. S. Stewart, Two-phase modeling of deflagration-to-detonation transition in granular materials: A critical examination of modeling issues, Physics of Fluids, vol.11, issue.2, pp.378-402, 1999.
DOI : 10.1063/1.869887

F. Coquel, T. Gallouët, J. Hérard, and N. Seguin, Closure laws for a two-fluid two-pressure model, Comptes Rendus Mathematique, vol.334, issue.10, pp.334927-932, 2002.
DOI : 10.1016/S1631-073X(02)02366-X

URL : https://hal.archives-ouvertes.fr/hal-01484345

F. Coquel, J. Hérard, K. Saleh, and N. Seguin, A Class of Two-fluid Two-phase Flow Models, 42nd AIAA Fluid Dynamics Conference and Exhibit, pp.2012-3356
DOI : 10.2514/6.2012-3356

P. Embid and M. Baer, Mathematical analysis of a two-phase continuum mixture theory, Continuum Mechanics and Thermodynamics, vol.10, issue.4, pp.279-312, 1992.
DOI : 10.1007/BF01129333

A. Forestier and S. Gavrilyuk, Criterion of hyperbolicity for non-conservative quasilinear systems admitting a partially convex conservation law, Mathematical Methods in the Applied Sciences, vol.14, issue.3, pp.2148-2158, 2011.
DOI : 10.1002/mma.1512

URL : https://hal.archives-ouvertes.fr/hal-01459988

T. Gallouët, J. Hérard, and N. Seguin, NUMERICAL MODELING OF TWO-PHASE FLOWS USING THE TWO-FLUID TWO-PRESSURE APPROACH, Mathematical Models and Methods in Applied Sciences, vol.14, issue.05, pp.663-700, 2004.
DOI : 10.1142/S0218202504003404

S. Gavrilyuk and R. Saurel, Mathematical and Numerical Modeling of Two-Phase Compressible Flows with Micro-Inertia, Journal of Computational Physics, vol.175, issue.1, pp.326-360, 2002.
DOI : 10.1006/jcph.2001.6951

J. Glimm, D. Saltz, and D. H. Sharp, Two-phase modelling of a fluid mixing layer, Journal of Fluid Mechanics, vol.378, pp.119-143, 1999.
DOI : 10.1017/S0022112098003127

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

S. K. Godunov, An interesting class of quasi-linear systems, Dokl. Akad. Nauk SSSR, vol.139, pp.521-523, 1961.

B. Hanouzet and R. Natalini, Global Existence of Smooth Solutions for Partially Dissipative Hyperbolic Systems with a Convex Entropy, Archive for Rational Mechanics and Analysis, vol.169, issue.2, pp.89-117, 2003.
DOI : 10.1007/s00205-003-0257-6

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

T. Kato, The Cauchy problem for quasi-linear symmetric hyperbolic systems, Archive for Rational Mechanics and Analysis, vol.168, issue.3, pp.181-205, 1975.
DOI : 10.1007/BF00280740

M. S. Mock, Systems of conservation laws of mixed type, Journal of Differential Equations, vol.37, issue.1, pp.70-88, 1980.
DOI : 10.1016/0022-0396(80)90089-3

V. Ransom and D. L. Hicks, Hyperbolic two-pressure models for two-phase flow, Journal of Computational Physics, vol.53, issue.1, p.124, 1984.
DOI : 10.1016/0021-9991(84)90056-1

W. Yong, Entropy and Global Existence for Hyperbolic Balance Laws, Archive for Rational Mechanics and Analysis, vol.172, issue.2, pp.247-266, 2004.
DOI : 10.1007/s00205-003-0304-3