G. Allaire, G. Faccanoni, and S. Kokh, A strictly hyperbolic equilibrium phase transition model, Comptes Rendus Mathematique, vol.344, issue.2, pp.135-140, 2007.
DOI : 10.1016/j.crma.2006.11.008
URL : https://hal.archives-ouvertes.fr/hal-00976919

Y. Brenier, Un algorithme rapide pour le calcul de transformées de Legendre- Fenchel discrètes, C. R. Acad. Sci. Paris Sér. I Math, vol.308, issue.20, pp.587-589, 1989.

L. Corrias, Fast Legendre???Fenchel Transform and Applications to Hamilton???Jacobi Equations and Conservation Laws, SIAM Journal on Numerical Analysis, vol.33, issue.4, pp.1534-1558, 1996.
DOI : 10.1137/S0036142993260208

P. Helluy and N. Seguin, Relaxation models of phase transition flows, ESAIM: Mathematical Modelling and Numerical Analysis, vol.40, issue.2, pp.331-352, 2006.
DOI : 10.1051/m2an:2006015
URL : https://hal.archives-ouvertes.fr/hal-00139607

J. Hiriart-urruty and C. Lemaréchal, Fundamentals of convex analysis. Grundlehren Text Editions, 2001.

S. Jaouen, Etude mathématique et numérique de stabilité pour des modèles hydrodynamiques avec transition de phase, 2001.

V. N. Kolokoltsov, . Maslov, and P. Victor, Idempotent analysis and its applications Mathematics and its Applications, 401, 1997.

Y. Lucet, A fast computational algorithm for the Legendre-Fenchel transform, Computational Optimization and Applications, vol.311, issue.3, pp.27-57, 1996.
DOI : 10.1007/BF00248008

Y. Lucet, Faster than the fast Legendre transform, the linear-time Legendre transform, Numerical Algorithms, vol.16, issue.2, pp.171-185, 1997.
DOI : 10.1023/A:1019191114493

V. Maslov, Méthodes opératorielles. (French) [Operator methods] Translated from the Russian by Djilali Embarek. ´ Editions Mir, 1987.

]. Maxplus, . Inria-max-plus, R. Menikoff, . Plohr, and J. Bradley, Home page: http://maxplus.saclay.inria.fr/ index.fr.html The Riemann problem for fluid flow of real materials, Reviews of Modern Physics, vol.61, issue.1, pp.75-130, 1989.