, the fixed-point problem is well posed for each intersection v on, By definition of T N

S. Adimurthi, G. D. Mishra, and . Veerappa-gowda, Explicit Hopf-Lax type formulas for Hamilton-Jacobi equations and conservation laws with discontinuous coefficients, J. Differential Equations, issue.1, pp.1-31, 2007.

D. Amadori and G. Guerra, Global BV solutions and relaxation limit for a system of conservation laws, Proc. Roy. Soc. Edinburgh Sect. A, vol.131, issue.1, pp.1-26, 2001.

L. Ambrosio, N. Fusco, and D. Pallara, Functions of bounded variation and free discontinuity problems, Oxford Mathematical Monographs, 2000.

F. Ancona and P. Goatin, Uniqueness and stability of L ? solutions for Temple class systems with boundary and properties of the attainable sets, SIAM J. Math. Anal, vol.34, issue.1, pp.28-63, 2002.

L. A. Anderson, Data-Driven Methods for Improved Estimation and Control of an Urban Arterial Traffic Network, 2015.

B. Andreianov, C. Donadello, and M. D. Rosini, A second-order model for vehicular traffics with local point constraints on the flow, Math. Models Methods Appl. Sci, vol.26, issue.4, pp.751-802, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01146116

J. Aubin, A. M. Bayen, and P. Saint-pierre, Dirichlet problems for some Hamilton-Jacobi equations with inequality constraints, SIAM J. Control Optim, vol.47, issue.5, pp.2348-2380, 2008.

A. Aw, A. Klar, T. Materne, and M. Rascle, Derivation of continuum traffic flow models from microscopic follow-the-leader models, SIAM J. Appl. Math, vol.63, issue.1, pp.259-278, 2002.

A. Aw and M. Rascle, Resurrection of "second order" models of traffic flow, SIAM J. Appl. Math, vol.60, issue.3, pp.916-938, 2000.

P. Bagnerini and M. Rascle, A multiclass homogenized hyperbolic model of traffic flow, SIAM J. Math. Anal, vol.35, issue.4, pp.949-973, 2003.

P. Baiti and A. Bressan, The semigroup generated by a Temple class system with large data, Differential Integral Equations, vol.10, issue.3, pp.401-418, 1997.

M. Bando, K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama, Dynamical model of traffic congestion and numerical simulation, Phys. Rev. E, vol.51, pp.1035-1042, 1995.

C. Bardos, A. Y. Le-roux, and J. Nédélec, First order quasilinear equations with boundary conditions, Comm. Partial Differential Equations, vol.4, issue.9, pp.1017-1034, 1979.

S. Benzoni-gavage and R. M. Colombo, An n-populations model for traffic flow, European J. Appl. Math, vol.14, issue.5, pp.587-612, 2003.

R. Borsche, R. M. Colombo, and M. Garavello, Mixed systems: ODEs -balance laws, J. Differential Equations, vol.252, issue.3, pp.2311-2338, 2012.

S. Boyd and L. Vandenberghe, Convex optimization, 2004.

M. Brackstone and M. Mcdonald, Car-following: a historical review, Transportation Research Part F: Traffic Psychology and Behaviour, vol.2, issue.4, pp.181-196, 1999.

A. Bressan, Global solutions of systems of conservation laws by wave-front tracking, J. Math. Anal. Appl, vol.170, issue.2, pp.414-432, 1992.

A. Bressan, The unique limit of the Glimm scheme, Arch. Rational Mech. Anal, vol.130, issue.3, pp.205-230, 1995.

A. Bressan, Hyperbolic systems of conservation laws, Oxford Lecture Series in Mathematics and its Applications, vol.20, 2000.

A. Bressan and R. M. Colombo, The semigroup generated by 2 × 2 conservation laws, Arch. Rational Mech. Anal, vol.133, issue.1, pp.1-75, 1995.

A. Bressan and R. M. Colombo, Decay of positive waves in nonlinear systems of conservation laws, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.26, issue.4, pp.133-160, 1998.

A. Bressan, G. Crasta, and B. Piccoli, Well-posedness of the Cauchy problem for n×n systems of conservation laws, Mem. Amer. Math. Soc, vol.146, issue.694, p.134, 2000.

A. Bressan and P. Goatin, Oleinik type estimates and uniqueness for n × n conservation laws, J. Differential Equations, vol.156, issue.1, pp.26-49, 1999.

A. Bressan and P. Goatin, Stability of L ? solutions of Temple class systems, Differential Integral Equations, vol.13, pp.1503-1528, 2000.

A. Bressan and P. Lefloch, Uniqueness of weak solutions to systems of conservation laws, Arch. Rational Mech. Anal, vol.140, issue.4, pp.301-317, 1997.

A. Bressan and K. T. Nguyen, Conservation law models for traffic flow on a network of roads, Netw. Heterog. Media, vol.10, issue.2, pp.255-293, 2015.

A. Bressan and K. T. Nguyen, Optima and equilibria for traffic flow on networks with backward propagating queues, Netw. Heterog. Media, vol.10, issue.4, pp.717-748, 2015.

A. Bressan and A. Nordli, The Riemann solver for traffic flow at an intersection with buffer of vanishing size, Netw. Heterog. Media, vol.12, issue.2, pp.173-189, 2017.

A. Bressan and T. Yang, A sharp decay estimate for positive nonlinear waves, SIAM J. Math. Anal, vol.36, issue.2, pp.659-677, 2004.

A. Bressan and F. Yu, Continuous Riemann solvers for traffic flow at a junction, Discrete Contin. Dyn. Syst, vol.35, issue.9, pp.4149-4171, 2015.

G. Bretti, R. Natalini, and B. Piccoli, A fluid-dynamic traffic model on road networks, Arch. Comput. Methods Eng, vol.14, issue.2, pp.139-172, 2007.

S. Calvert, M. Minderhoud, H. Taale, I. Wilmink, and V. Knoop, Traffic assignment and simulation models, 2016.

E. S. Canepa and C. G. Claudel, Exact solutions to traffic density estimation problems involving the lighthill-whitham-richards traffic flow model using mixed integer programming, 15th International IEEE Conference on Intelligent Transportation Systems, pp.832-839, 2012.

C. Chalons, M. L. Delle-monache, and P. Goatin, A conservative scheme for nonclassical solutions to a strongly coupled PDE-ODE problem, Interfaces and Free Boundaries, vol.19, issue.4, pp.553-570, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01070262

C. Chalons and P. Goatin, Godunov scheme and sampling technique for computing phase transitions in traffic flow modeling, Interfaces Free Bound, vol.10, issue.2, pp.197-221, 2008.

R. E. Chandler, R. Herman, and E. W. Montroll, Traffic dynamics: Studies in car following, Operations Research, vol.6, issue.2, pp.165-184, 1958.

G. Q. Chen, C. D. Levermore, and T. Liu, Hyperbolic conservation laws with stiff relaxation terms and entropy, Comm. Pure Appl. Math, vol.47, issue.6, pp.787-830, 1994.

G. Q. Chen and T. Liu, Zero relaxation and dissipation limits for hyperbolic conservation laws, Comm. Pure Appl. Math, vol.46, issue.5, pp.755-781, 1993.

C. Christoforou and K. Trivisa, Sharp decay estimates for hyperbolic balance laws, J. Differential Equations, vol.247, issue.2, pp.401-423, 2009.

C. Christoforou and K. Trivisa, Decay of positive waves of hyperbolic balance laws, Acta Math. Sci. Ser. B Engl. Ed, vol.32, issue.1, pp.352-366, 2012.

C. G. Claudel and A. M. Bayen, Lax-Hopf based incorporation of internal boundary conditions into Hamilton-Jacobi equation. Part I: Theory, IEEE Trans. Automat. Control, vol.55, issue.5, pp.1142-1157, 2010.

C. G. Claudel and A. M. Bayen, Lax-Hopf based incorporation of internal boundary conditions into Hamilton-Jacobi equation. Part II: Computational methods, IEEE Trans. Automat. Control, vol.55, issue.5, pp.1158-1174, 2010.

G. M. Coclite, M. Garavello, and B. Piccoli, Traffic flow on a road network, SIAM J. Math. Anal, vol.36, issue.6, pp.1862-1886, 2005.

R. M. Colombo, Hyperbolic phase transitions in traffic flow, SIAM J. Appl. Math, vol.63, issue.2, pp.708-721, 2002.

R. M. Colombo and A. Corli, Well posedness for multilane traffic models, Ann. Univ. Ferrara Sez. VII Sci. Mat, vol.52, issue.2, pp.291-301, 2006.

R. M. Colombo, P. Goatin, and F. S. Priuli, Global well posedness of traffic flow models with phase transitions, Nonlinear Anal, vol.66, issue.11, pp.2413-2426, 2007.

R. M. Colombo, P. Goatin, and M. D. Rosini, On the modelling and management of traffic, ESAIM Math. Model. Numer. Anal, vol.45, issue.5, pp.853-872, 2011.

R. M. Colombo and A. Marson, A Hölder continuous ode related to traffic flow, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, vol.133, issue.4, pp.759-772, 2003.

R. Courant and K. O. Friedrichs, Supersonic Flow and Shock Waves, 1948.

M. G. Crandall and P. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc, vol.277, issue.1, pp.1-42, 1983.

G. Crasta and B. Piccoli, Viscosity solutions and uniqueness for systems of inhomogeneous balance laws, Discrete Contin. Dynam. Systems, vol.3, issue.4, pp.477-502, 1997.

E. Cristiani and F. S. Priuli, A destination-preserving model for simulating Wardrop equilibria in traffic flow on networks, Netw. Heterog. Media, vol.10, issue.4, pp.857-876, 2015.

C. M. Dafermos, Polygonal approximations of solutions of the initial value problem for a conservation law, J. Math. Anal. Appl, vol.38, pp.33-41, 1972.

C. M. Dafermos, Uniqueness of Zero Relaxation Limit, SIAM J. Math. Anal, vol.51, issue.3, pp.1999-2018, 2019.

C. F. Daganzo, Requiem for second-order fluid approximations of traffic flow, Transportation Research Part B: Methodological, vol.29, issue.4, pp.277-286, 1995.

C. D'apice and B. Piccoli, Vertex flow models for vehicular traffic on networks, Math. Models Methods Appl. Sci, vol.18, pp.1299-1315, 2008.

M. L. Delle-monache and P. Goatin, Scalar conservation laws with moving constraints arising in traffic flow modeling: an existence result, J. Differential Equations, vol.257, issue.11, pp.4015-4029, 2014.
URL : https://hal.archives-ouvertes.fr/hal-00976855

R. J. Diperna, Global existence of solutions to nonlinear hyperbolic systems of conservation laws, J. Differential Equations, vol.20, issue.1, pp.187-212, 1976.

, European urban mobility: Policy context. Publications Office of the European Union, 2017.

, Sustainable urban mobility: European policy, practice and solutions. Publications Office of the European Union, 2017.

N. S. Dymski, P. Goatin, and M. D. Rosini, Existence of BV solutions for a nonconservative constrained Aw-Rascle-Zhang model for vehicular traffic, J. Math. Anal. Appl, vol.467, issue.1, pp.45-66, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01713987

L. C. Evans, Partial differential equations, Graduate Studies in Mathematics, vol.19, 2010.

S. Fan, M. Herty, and B. Seibold, Comparative model accuracy of a data-fitted generalized Aw-Rascle-Zhang model, Netw. Heterog. Media, vol.9, issue.2, pp.239-268, 2014.

H. Frankowska, On LeFloch's solutions to the initial-boundary value problem for scalar conservation laws, J. Hyperbolic Differ. Equ, vol.7, issue.3, pp.503-543, 2010.

M. Garavello and P. Goatin, The Cauchy problem at a node with buffer, Discrete Contin. Dyn. Syst, vol.32, issue.6, pp.1915-1938, 2012.
URL : https://hal.archives-ouvertes.fr/inria-00556954

M. Garavello, K. Han, and B. Piccoli, Models for vehicular traffic on networks, AIMS Series on Applied Mathematics, vol.9, 2016.

M. Garavello and B. Piccoli, Source-destination flow on a road network, Commun. Math. Sci, vol.3, issue.3, pp.261-283, 2005.

M. Garavello and B. Piccoli, Traffic flow on networks, AIMS Series on Applied Mathematics. American Institute of Mathematical Sciences, vol.1, 2006.

M. Garavello and B. Piccoli, Conservation laws on complex networks, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.26, issue.5, pp.1925-1951, 2009.

M. Garavello and B. Piccoli, A multibuffer model for LWR road networks, Advances in dynamic network modeling in complex transportation systems, vol.2, pp.143-161, 2013.

D. C. Gazis, A Wiley-Interscience publication, 1974.

D. C. Gazis, R. Herman, and R. W. Rothery, Nonlinear follow-the-leader models of traffic flow, Operations Research, vol.9, issue.4, pp.545-567, 1961.

F. Giorgi, L. Leclercq, and J. Lesort, A traffic flow model for urban traffic analysis: extensions of the LWR model for urban and environmental applications, Transportation and Traffic Theory in the 21st Century: Proceedings of the 15th International Symposium on Transportation and Traffic Theory, pp.393-415, 2002.

J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math, vol.18, pp.697-715, 1965.

P. Goatin, The Aw-Rascle vehicular traffic flow model with phase transitions, Math. Comput. Modelling, vol.44, issue.3-4, pp.287-303, 2006.

P. Goatin and L. Gosse, Decay of positive waves for n × n hyperbolic systems of balance laws, Proc. Amer. Math. Soc, vol.132, issue.6, pp.1627-1637, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00419731

P. Goatin and N. Laurent-brouty, The zero relaxation limit for the Aw-Rascle-Zhang traffic flow model, Z. Angew. Math. Phys, vol.70, issue.1, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01760930

E. Godlewski and P. Raviart, Numerical approximation of hyperbolic systems of conservation laws, Applied Mathematical Sciences, vol.118, 1996.

S. Göttlich, M. Herty, and A. Klar, Network models for supply chains, Commun. Math. Sci, vol.3, issue.4, pp.545-559, 2005.

J. M. Greenberg, Extensions and amplifications of a traffic model of Aw and Rascle, SIAM J. Appl. Math, vol.62, issue.3, p.2, 2001.

J. M. Greenberg, A. Klar, and M. Rascle, Congestion on multilane highways, SIAM J. Appl. Math, vol.63, issue.3, pp.818-833, 2003.

B. Greenshields, J. Bibbins, W. Channing, and H. Miller, A study of traffic capacity. Highway Research Board proceedings, 1935.

M. Gugat, A. Keimer, G. Leugering, and Z. Wang, Analysis of a system of nonlocal conservation laws for multi-commodity flow on networks, Netw. Heterog. Media, vol.10, issue.4, pp.749-785, 2015.

K. Han, B. Piccoli, and W. Szeto, Continuous-time link-based kinematic wave model: formulation, solution existence, and well-posedness, Transportmetrica B: Transport Dynamics, vol.4, issue.3, pp.187-222, 2016.

D. Helbing, Improved fluid-dynamic model for vehicular traffic, Phys. Rev. E, vol.51, pp.3164-3169, 1995.

M. Herty and A. Klar, Modeling, simulation, and optimization of traffic flow networks, SIAM J. Sci. Comput, vol.25, issue.3, pp.1066-1087, 2003.

M. Herty, A. Klar, and B. Piccoli, Existence of solutions for supply chain models based on partial differential equations, SIAM J. Math. Anal, vol.39, issue.1, pp.160-173, 2007.

M. Herty, J. Lebacque, and S. Moutari, A novel model for intersections of vehicular traffic flow, Netw. Heterog. Media, vol.4, issue.4, pp.813-826, 2009.

D. Hoff, Invariant regions for systems of conservation laws, Trans. Amer. Math. Soc, vol.289, issue.2, pp.591-610, 1985.

H. Holden and N. H. Risebro, A mathematical model of traffic flow on a network of unidirectional roads, SIAM J. Math. Anal, vol.26, issue.4, pp.999-1017, 1995.

H. Holden and N. H. Risebro, Models for dense multilane vehicular traffic, 2018.

H. K. Jenssen and C. Sinestrari, On the spreading of characteristics for non-convex conservation laws, Proc. Roy. Soc. Edinburgh Sect. A, vol.131, issue.4, pp.909-925, 2001.

K. T. Joseph and G. D. Gowda, Explicit formula for the solution of convex conservation laws with boundary condition, Duke Math. J, vol.62, issue.2, pp.401-416, 1991.

A. Keimer, N. Laurent-brouty, F. Farokhi, H. Signargout, V. Cvetkovic et al., Information patterns in the modeling and design of mobility management services, Proceedings of the IEEE, vol.106, issue.4, pp.554-576, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01656767

B. S. Kerner, Phase transitions in traffic flow, Traffic and Granular Flow '99, pp.253-283, 2000.

A. Klar and R. Wegener, Kinetic Traffic Flow Models, Birkhäuser Boston, pp.263-316, 2000.

S. N. Kru?kov, First order quasilinear equations with several independent variables. Mat. Sb, vol.81, pp.228-255, 1970.

C. Lattanzio and P. Marcati, The zero relaxation limit for the hydrodynamic Whitham traffic flow model, J. Differential Equations, vol.141, issue.1, pp.150-178, 1997.

C. Lattanzio, A. Maurizi, and B. Piccoli, Moving bottlenecks in car traffic flow: a PDE-ODE coupled model, SIAM J. Math. Anal, vol.43, issue.1, pp.50-67, 2011.

N. Laurent-brouty, G. Costeseque, and P. Goatin, A coupled PDE-ODE model for bounded acceleration in macroscopic traffic flow models. IFAC-PapersOnLine, 15th IFAC Symposium on Control in Transportation Systems, vol.51, pp.37-42, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01636156

N. Laurent-brouty, G. Costeseque, and P. Goatin, A macroscopic traffic flow model accounting for bounded acceleration, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02155131

N. Laurent-brouty, A. Keimer, P. Goatin, and A. M. Bayen, A macroscopic traffic flow model with finite buffers on networks: Well-posedness by means of Hamilton-Jacobi equations, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02121812

P. Lax, Shock waves and entropy, pp.603-634, 1971.

P. D. Lax, Hyperbolic systems of conservation laws, II. Comm. Pure Appl. Math, vol.10, pp.537-566, 1957.

J. Lebacque, A finite acceleration scheme for first order macroscopic traffic flow models. IFAC Proceedings Volumes, vol.30, pp.787-792, 1997.

J. Lebacque, A two phase extension of the LWR Model based on the boundedness of traffic acceleration, Transportation and Traffic Theory in the 21st Century, pp.697-718, 2002.

J. Lebacque, Two-phase bounded-acceleration traffic flow model: analytical solutions and applications, Transportation Research Record: Journal of the Transportation Research Board, issue.1852, pp.220-230, 2003.

J. Lebacque, H. Haj-salem, and S. Mammar, Second order traffic flow modeling: supply-demand analysis of the inhomogeneous riemann problem and of boundary conditions, Proceedings of the 10th Euro Working Group on Transportation (EWGT), vol.3, 2005.

J. Lebacque, J. Lesort, and F. Giorgi, Introducing buses into first-order macroscopic traffic flow models, Transportation Research Record: Journal of the Transportation Research Board, vol.1644, issue.1, pp.70-79, 1998.

J. Lebacque, S. Mammar, and H. H. Salem, Generic second order traffic flow modelling, Transportation and Traffic Theory, 2007.

L. Leclercq, Modélisation dynamique du trafic et applications à l'estimation du bruit routier, 2002.

L. Leclercq, Bounded acceleration close to fixed and moving bottlenecks, Transportation Research Part B: Methodological, vol.41, issue.3, pp.309-319, 2007.

L. Leclercq, A new numerical scheme for bounding acceleration in the LWR model, 4th IMA International Conference on Mathematics in Transport, 2007.

G. Leoni, A first course in Sobolev spaces, volume 105 of Graduate Studies in Mathematics, 2009.

R. J. Leveque, Finite volume methods for hyperbolic problems, Cambridge Texts in Applied Mathematics, 2002.

R. J. Leveque and B. Temple, Stability of Godunov's method for a class of 2 × 2 systems of conservation laws, Trans. Amer. Math. Soc, vol.288, issue.1, pp.115-123, 1985.

T. Li, Global solutions of nonconcave hyperbolic conservation laws with relaxation arising from traffic flow, J. Differential Equations, vol.190, issue.1, pp.131-149, 2003.

T. Liard and B. Piccoli, Well-Posedness for Scalar Conservation Laws with Moving Flux Constraints, SIAM J. Appl. Math, vol.79, issue.2, pp.641-667, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01684506

M. J. Lighthill and G. B. Whitham, On kinematic waves. II. A theory of traffic flow on long crowded roads, Proc. Roy. Soc. London. Ser. A, vol.229, pp.317-345, 1955.

A. D. May, Traffic flow fundamentals, 1990.

O. A. Ole?nik, Discontinuous solutions of non-linear differential equations, N.S.), vol.12, issue.3, pp.3-73, 1957.

O. A. Ole?nik, On the uniqueness of the generalized solution of the Cauchy problem for a non-linear system of equations occurring in mechanics. Uspehi Mat. Nauk, N.S.), vol.12, issue.6, pp.169-176, 1957.

O. A. Ole?nik, Discontinuous solutions of non-linear differential equations, Amer. Math. Soc. Transl, vol.26, issue.2, pp.95-172, 1963.

B. G. Pachpatte, Inequalities for differential and integral equations, Mathematics in Science and Engineering, vol.197, 1998.

H. J. Payne, Models of freeway traffic and control. Mathematical models of public systems, 1971.

S. Peeta and A. K. Ziliaskopoulos, Foundations of dynamic traffic assignment: The past, the present and the future, Networks and Spatial Economics, vol.1, issue.3, pp.233-265, 2001.

L. A. Pipes, An operational analysis of traffic dynamics, Journal of Applied Physics, vol.24, issue.3, pp.274-281, 1953.

I. Prigogine, A Boltzmann-like approach to the statistical theory of traffic flow, Theory of traffic flow, pp.158-164, 1961.

I. Prigogine and F. C. Andrews, A Boltzmann-like approach for traffic flow, Operations Res, vol.8, pp.789-797, 1960.

I. Prigogine and R. Herman, Kinetic theory of vehicular traffic, 1971.

M. Rascle, An improved macroscopic model of traffic flow: derivation and links with the Lighthill-Whitham model, Math. Comput. Modelling, vol.35, issue.5-6, pp.581-590, 2002.

A. , Fahrzeugbewegungen in der kolonne, Osterreichisches Ingenieur Archiv, vol.4, pp.193-215, 1950.

P. I. Richards, Shock waves on the highway, Operations Res, vol.4, pp.42-51, 1956.

N. H. Risebro, A front-tracking alternative to the random choice method, Proc. Amer. Math. Soc, vol.117, issue.4, pp.1125-1139, 1993.

S. Samaranayake, W. Krichene, J. Reilly, M. L. Monache, P. Goatin et al., Discrete-time system optimal dynamic traffic assignment (SO-DTA) with partial control for physical queuing networks, Transportation Science, vol.52, issue.4, pp.982-1001, 2018.

D. Serre, Systèmes de lois de conservation II. structures géométriques, oscillation et problèmes mixtes, 1996.

B. Temple, Systems of conservation laws with invariant submanifolds, Trans. Amer. Math. Soc, vol.280, issue.2, pp.781-795, 1983.

J. Thai, N. Laurent-brouty, and A. M. Bayen, Negative externalities of gps-enabled routing applications: A game theoretical approach, IEEE 19th International Conference on Intelligent Transportation Systems (ITSC), pp.595-601, 2016.

M. Treiber and A. Kesting, Traffic flow dynamics, 2013.

S. Villa, P. Goatin, and C. Chalons, Moving bottlenecks for the Aw-Rascle-Zhang traffic flow model, Discrete Contin. Dyn. Syst. Ser. B, vol.22, issue.10, pp.3921-3952, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01347925

D. H. Wagner, Equivalence of the Euler and Lagrangian equations of gas dynamics for weak solutions, J. Differential Equations, vol.68, issue.1, pp.118-136, 1987.

G. B. Whitham, Linear and nonlinear waves. pages xvi+636, Pure and Applied Mathematics, 1974.

G. C. Wong and S. C. Wong, A multi-class traffic flow model -an extension of lwr model with heterogeneous drivers, Transportation Research Part A: Policy and Practice, vol.36, issue.9, pp.827-841, 2002.

E. Zeidler, Applied functional analysis, Applied Mathematical Sciences, vol.108, 1995.

H. M. Zhang, A non-equilibrium traffic model devoid of gas-like behavior, Transportation Research Part B: Methodological, vol.36, issue.3, pp.275-290, 2002.