References. [1] R. Colombo, F. Marcellini and M. Rascle. A 2-Phase Trac Model based on a Speed Bound SIAM J. Appl. Math,Vol 70,(2010),

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1 References [1] R. Colombo, F. Marcellini and M. Rascle. A 2-Phase Trac Model based on a Speed Bound SIAM J. Appl. Math,Vol 70,(2010), [2] F. Siebel, W. Mauser, S. Moutari and M. Rascle. balanced vehicular trac ow at a bottleneck Math. and Computer Modelling,Vol 49,(2009), [3] M. Herty, C. Kirchner, S. Moutari and M. Rascle. Multicommodity ows on road networks. Commun. Math. Sci., Vol 6,1 (2008), [4] F. Berthelin, P. Degond, V. Le Blanc, S. Moutari, M. Rascle and J. Royer A Trac Flow Model with Constraints for the Modeling of Trac Jams. Math. Models and Methods in Appl. Sciences,Vol 18,1 (2008), [5] S. Moutari and M. Rascle. A Hybrid Lagrangian model based on the Aw- Rascle Trac Flow model. SIAM J. Appl. Math., Vol 68,2 (2007), [6] F. Berthelin, M. Delitala, P. Degond and M. Rascle. A model for the formation and evolution of trac jams. Arch.Rat. Mechanics and Anal., 187(2008), [7] K. Karlsen, M. Rascle and E. Tadmor. On the existence and compactness of a two-dimensional resonant system of conservation laws. Commun. Math. Sci. Volume 5, 2, , [8] M. Herty, M. Rascle and S. Moutari Optimization Criteria for Modelling Intersections of Vehicular Trac Flow, Network and Heterogenous Media, (2006)Vol 1, 2, [9] M. Herty and M. Rascle. Coupling conditions for a class of "secondorder" models for trac ow. SIAM J. Math. Anal, Vol 38 (2006), [10] G.Q. Chen, S. Junca and M. Rascle. Validity of nonlinear geometric optics for entropy solutions of multidimensional scalar conservation laws. J. Di. Eq., (2006), Vol 222, 2, [11] E. Tadmor, M. Rascle and P. Bagnerini. Compensated compactness for 2D conservation laws. J. of Hyperbolic Di. Eq., (2005),vol 2, 3,

Degond, V. Le Blanc, S. Moutari, M. Rascle and J. Royer A Trac Flow Model with Constraints for the Modeling of Trac Jams. Math. Models and Methods in Appl. Sciences,Vol 18,1 (2008),1269-1298. [5] S.

2 [12] P. Bagnerini and M. Rascle. A multi-class homogenized hyperbolic model of trac ow. SIAM J. Math. Anal., 35(4), [13] J. Greenberg, A. Klar, and M. Rascle. Congestion on multilane highways. SIAM J. Appl. Math., 63(3):818833, [14] M. Rascle. An improved macroscopic model of trac ow: derivation and links with the lightill-whitham model. Math. and Comp. Modelling, 35(5-6):581590, [15] A. Aw, A. Klar, T. Materne, and M. Rascle. Derivation of continuum trac ow models from microscopic Follow-the- Leader models. SIAM J. Applied Math., 63(1):259278, [16] Ph. Hoch and M. Rascle. Hamilton- Jacobi equations on a manifold and applications to grid generation or renement. SIAM J. Sc. Comput., 23(6): , [17] S. Junca and M. Rascle. Strong relaxation of the isothermal Euler system to the heat equation. Zeitschr. Angew. Math. Phys., 53(2): , [18] P. Bagnerini, Ph. Hoch, and M. Rascle (*). The eikonal equation on a manifold. Applications to grid generation or renement. In G. Warnecke and H. Freistuhler, editors, 8th Int. Conf. Hyperbolic Problems, Magdeburg, 2000, number 140, pages Birkhaï¾ 1 2ser, [19] A. Aw and M. Rascle. Resurrection of "second order" models of trac ow? SIAM J. Appl. Math., 60(3):916938, [20] G. Q. Chen and M. Rascle. Initial layers and uniqueness of weak entropy solutions to hyperbolic conservation laws. Arch. Rat. mech. Anal., 153:205220, [21] S. Junca and M. Rascle. Relaxation of the isothermal Euler-Poisson system to the drift-diusion equations. Quart. of Appl. Math., 58(3): , [22] Ph. Hoch and M. Rascle. A numerical study of a pathological example of p-system. SIAM J. Num. Analysis, 36(5): , [23] F. Poupaud and M. Rascle. Measure solutions to the linear multidimensional transport equation with non-smooth coecients. Comm. Part. Di. Eq., 22:337358,

Modelling, 35(5-6):581590, 2002. [15] A. Aw, A. Klar, T. Materne, and M. Rascle. Derivation of continuum trac ow models from microscopic Follow-the- Leader models. SIAM J. Applied Math.

3 [24] J.F. Collet and M. Rascle. Convergence of the relaxation approximation to a scalar nonlinear hyperbolic equation arising in chromatography. Zeitschrift Angew. Math. und Phys., 47:399409, [25] M. Rascle (*). Global existence of L 2 solutions in dynamical elastoplasticity. Matématica Contemporânea,Rio, 11:121134, [26] M. Rascle (*). Elasto-plasticity as a zero-relaxation limit of elastic visco-plasticity. Transport Theory and Statistical physics, 25(3-5): , Proceedings. [27] A. Nouri and M. Rascle. A global existence and uniqueness theorem for a model problem in dynamic elasto-plasticity with isotropic strainhardening. SIAM Journal Math. Anal., 26(4):850868, [28] F. Poupaud, M. Rascle, and J.P. Vila. Global solutions to the isothermal euler-poisson system with arbitrarily large data. J. Di. Equations, 123(1):93121, [29] M. Rascle and C. Ziti. Finite time blow-up in some models of chemotaxis. J. Math. Biology, (33):388414, [30] J. Greenberg and M. Rascle. Time-periodic solutions to conservation laws. Arch. Rat. Mech. Anal., 115:395407, [31] M. Rascle. On the static and dynamic study of oscillations for some hyperbolic systems of conservation laws. Ann. Inst. Henri Poincaré, 8(3-4):333350, [32] M. Rascle, D. Serre, and M. Slemrod, editors (*). Partial Dierential Equations and Continuum Models of Phase Transitions, volume 344 of Lecture Notes in Physics. Springer, [33] M. Rascle (*). Convergence of approximate solutions to some systems of conservation laws: a conjecture on the product of the Riemann invariants. In C.M. Dafermos and Slemrod, editors, Oscillations theory, computation and method of compensated compactness, volume 2 of IMA, pages IMA, Springer, [34] M. Rascle (*). On the convergence of the viscosity method for the system of nonlinear 1- D elasticity. In B. Nicolaenko et al, editor, AMS Santa-Fe Summer School on nonlinear PDE, volume 23 of Lectures in Appl. Math., pages Amer. Math. Soc.,

Transport Theory and Statistical physics, 25(3-5):477 489, 1996. Proceedings. [27] A. Nouri and M. Rascle.

4 [35] C. Carasso, M.Rascle, and D.Serre. Etude d'un modèle hyperbolique en dynamique des câbles. Modél. math. et Anal. Num'er., 19(4):573599, [36] M. Rascle (*). Sur quelques problèmes mathématiques dans l'étude théorique du chimiotactisme. In J. Demongeot, editor, Quatrième Séminaire de Biologie Théorique, pages Editions du CNRS, [37] M. Rascle. The Riemann problem for a nonlinear non-strictly hyperbolic problem arising in Biology. Comp. and Math. with Applic., 11(1-3): , [38] M. Rascle and D. Serre. Compacité par compensation et systèmes hyperboliques de lois de conservation. Compt. Rend. Acad. Sciences, 299,Série 1:673676, [39] M. Rascle (*). On some "viscous" perturbations of quasi-linear rst order hyperbolic systems arising in biology. In J.A. Smoller, editor, Conference on Nonlinear PDE, volume 17 of Contempor. Math., pages Amer. Math. Soc., [40] M. Rascle. Perturbations par viscosité de certains systèmes hyperboliques non linéaires. PhD thesis, Thèse d'etat,univ. Lyon 1, [41] M. Rascle (*). On a system of nonlinear strongly coupled PDE arising in biology. In W.N. Everitt-B.D. Sleeman, editor, International Conference on Ordinary and Partial Dierential Equations, volume 846 of Lectures Notes in Mathematics, pages Dundee, Springer. [42] M. Rascle. Sur une équation non linéaire issue de la biologie. J. Di. Eq., 32(3):420453, [43] M. Rascle (*). Sur certains systèmes d'edp non linéaires fortement couplées issues de la biologie. In C. Chevalet-A. Micali, editor, Modèles mathématiques en biologie, volume 41 of Lectures Notes in Biomathematics, pages Springer. [44] M. Rascle. Sur un problème non linéaire issu de la biologie. Compt. Rend. Acad. Sciences, 286, Série A:555558, [45] M. Rascle and F. Robert. Contraction faible en norme vectorielle. Linear Algebra and its Applications, 6:305335,

The Riemann problem for a nonlinear non-strictly hyperbolic problem arising in Biology. Comp. and Math. with Applic., 11(1-3):223 238, 1985. [38] M. Rascle and D. Serre.

5 [46] M. Rascle. Théorie de Perron-Frobenius de certains opérateurs monotones non linéaires dans un espace de Riesz normé complet, Thèse de Troisième cycle, Univ. Lyon 1,

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