References
- 1. R. M. Colombo, F. Marcellini, and M. Rascle, A 2-phase trafic model based on a speed bound, SIAM J. Appl. Math., vol. 70, no. 7, pp. 2652-2666, 2010.
- 2. S. Blandin, D. Work, P. Goatin, B. Piccoli, and A. Bayen, A general phase transition model for vehicular trafic, SIAM J. Appl. Math., vol. 71, no. 1, pp. 107-127, 2011.
- 3. M. J. Lighthill and G. B. Whitham, On kinematic waves. II. A theory of trafic ow on long crowded roads, Proc. Roy. Soc. London. Ser. A., vol. 229, pp. 317-345, 1955.
- 4. P. I. Richards, Shock waves on the highway, Operations Res., vol. 4, pp. 42-51, 1956.
- 5. B. S. Kerner, The physics of trafic: empirical freeway pattern features, engineering applications, and theory. Springer, 2012.
- 6. R. M. Colombo, Hyperbolic phase transitions in trafic ow., SIAM J. Appl. Math., vol. 63, no. 2, pp. 708-721, 2002.
- 7. R. M. Colombo, Phase transitions in hyperbolic conservation laws, in Progress in analysis, Vol. I, II (Berlin, 2001), pp. 1279-1287, World Sci. Publ., River Edge, NJ, 2003.
- 8. R. M. Colombo, P. Goatin, and F. S. Priuli, Global well posedness of trafic ow models with phase transitions, Nonlinear Anal., vol. 66, no. 11, pp. 2413-2426, 2007.
- 9. P. Goatin, The Aw-Rascle vehicular trafic ow model with phase transitions, Math. Comput. Modelling, vol. 44, no. 3-4, pp. 287-303, 2006.
- 10. J. P. Lebacque, X. Louis, S. Mammar, B. Schnetzlera, and H. Haj-Salem, Modélisation du trafic autoroutier au second ordre, Comptes Rendus Mathematique, vol. 346, pp. 1203-1206, November 2008.
- 11. F. Marcellini, Free-congested and micro-macro descriptions of trafic ow, Discrete Contin. Dyn. Syst. Ser. S, vol. 7, no. 3, pp. 543-556, 2014.
- 12. S. K. Godunov, A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics, Mat. Sb. (N.S.), vol. 47 (89), pp. 271-306, 1959.
- 13. R. J. LeVeque, Finite volume methods for hyperbolic problems. Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 2002.
- 14. C. Chalons and P. Goatin, Godunov scheme and sampling technique for computing phase transitions in trafic ow modeling, Interfaces Free Bound., vol. 10, no. 2, pp. 197-221, 2008.
- 15. X. Zhong, T. Y. Hou, and P. G. LeFloch, Computational methods for propagating phase boundaries, J. Comput. Phys., vol. 124, no. 1, pp. 192-216, 1996.
- 16. R. J. LeVeque, Numerical methods for conservation laws. Lectures in Mathematics ETH Zürich, Basel: Birkhäuser Verlag, second ed., 1992.
- 17. R. Courant, K. Friedrichs, and H. Lewy, On the partial difference equations of mathematical physics, IBM J. Res. Develop., vol. 11, pp. 215-234, 1967.