Conservation Laws on Complex Networks
Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 5, pp. 1925-1951.
@article{AIHPC_2009__26_5_1925_0,
     author = {Garavello, Mauro and Piccoli, Benedetto},
     title = {Conservation {Laws} on {Complex} {Networks}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1925--1951},
     publisher = {Elsevier},
     volume = {26},
     number = {5},
     year = {2009},
     doi = {10.1016/j.anihpc.2009.04.001},
     mrnumber = {2566716},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2009.04.001/}
}
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Garavello, Mauro; Piccoli, Benedetto. Conservation Laws on Complex Networks. Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 5, pp. 1925-1951. doi : 10.1016/j.anihpc.2009.04.001. http://archive.numdam.org/articles/10.1016/j.anihpc.2009.04.001/

[1] Aw A., Rascle M., Resurrection of “second Order” Models of Traffic Flow, SIAM J. Appl. Math. 60 (3) (2000) 916-938, (electronic). | MR | Zbl

[2] Banda M. K., Herty M., Klar A., Gas Flow in Pipeline Networks, Netw. Heterog. Media 1 (1) (2006) 41-56. | MR | Zbl

[3] Bardos C., Le Roux A. Y., Nédélec J. C., First Order Quasilinear Equations With Boundary Conditions, Comm. Partial Differential Equations 4 (1979) 1017-1034. | MR | Zbl

[4] Bastin G., Haut B., A Second Order Model of Arc Junctions in Fluid Models of Traffic Networks, Netw. Heterog. Media 2 (2) (2007) 227-253. | MR | Zbl

[5] Bayen A. M., Sun D., Strub I. S., Comparison of the Performance of Four Eulerian Network Flow Models for Strategic Air Traffic Management, Netw. Heterog. Media 2 (4) (2007) 569-595. | MR | Zbl

[6] Bellomo N., Coscia A., First Order Models and Closure of the Mass Conservation Equation in the Mathematical Theory of Vehicular Traffic Flow, C.R. Mecanique 333 (2005) 843-851. | Zbl

[7] Benzoni-Gavage S., Colombo R. M., An N-Populations Model for Traffic Flow, European J. Appl. Math. 14 (5) (2003) 587-612. | MR | Zbl

[8] Bressan A., A Contractive Metric for Systems of Conservation Laws With Coinciding Shock and Rarefaction Curves, J. Differential Equations 106 (1993) 332-366. | MR | Zbl

[9] Bressan A., Hyperbolic Systems of Conservation Laws. the One-Dimensional Cauchy Problem, Oxford Lecture Ser. Math. Appl., vol. 20, Oxford Univ. Press, Oxford, 2000. | MR | Zbl

[10] Bressan A., Crasta G., Piccoli B., Well-Posedness of the Cauchy Problem for n×n Systems of Conservation Laws, Mem. Amer. Math. Soc. 146 (694) (2000), viii+134. | MR | Zbl

[11] Chitour Y., Piccoli B., Traffic Circles Timing of Traffic Lights for Cars Flow, Discrete Contin. Dyn. Syst. Ser. B 5 (3) (2005) 599-630. | MR | Zbl

[12] Coclite G. M., Garavello M., Piccoli B., Traffic Flow on a Road Network, SIAM J. Math. Anal. 36 (6) (2005) 1862-1886. | MR | Zbl

[13] Colombo R. M., Hyperbolic Phase Transitions in Traffic Flow, SIAM J. Appl. Math. 63 (2) (2002) 708-721, (electronic). | MR | Zbl

[14] Colombo R. M., Garavello M., A Well Posed Riemann Problem for the P-System at a Junction, Netw. Heterog. Media 1 (3) (2006) 495-511. | MR | Zbl

[15] Colombo R. M., Garavello M., On the Cauchy Problem for the P-System at a Junction, SIAM J. Appl. Math. 39 (5) (2008) 1456-1471. | MR | Zbl

[16] R.M. Colombo, P. Goatin, B. Piccoli, Road network with phase transitions, preprint.

[17] Dafermos C. M., Hyperbolic Conservation Laws in Continuum Physics, Grundlehren Math. Wiss., vol. 325, second ed., Springer-Verlag, Berlin, 2005. | MR | Zbl

[18] D'Apice C., Manzo R., A Fluid Dynamic Model for Supply Chains, Netw. Heterog. Media 1 (3) (2006) 379-398. | MR | Zbl

[19] D'Apice C., Manzo R., Piccoli B., Packet Flow on Telecommunication Networks, SIAM J. Math. Anal. 38 (3) (2006) 717-740, (electronic). | MR | Zbl

[20] Dubois F., Lefloch P., Boundary Conditions for Nonlinear Hyperbolic Systems of Conservation Laws, J. Differential Equations 71 (1) (1988) 93-122. | MR | Zbl

[21] Garavello M., Natalini R., Piccoli B., Terracina A., Conservation Laws With Discontinuous Flux, Netw. Heterog. Media 2 (1) (2007) 159-179, (electronic). | MR | Zbl

[22] Garavello M., Piccoli B., Source-Destination Flow on a Road Network, Commun. Math. Sci. 3 (3) (2005) 261-283. | MR | Zbl

[23] Garavello M., Piccoli B., Traffic Flow on a Road Network Using the Aw-Rascle Model, Comm. Partial Differential Equations 31 (1-3) (2006) 243-275. | MR | Zbl

[24] Garavello M., Piccoli B., Traffic Flow on Networks, AIMS Ser. Appl. Math., vol. 1, AIMS, 2006. | MR | Zbl

[25] Goatin P., The Aw-Rascle Vehicular Traffic Flow Model With Phase Transitions, Math. Comput. Modelling 44 (3-4) (2006) 287-303. | MR | Zbl

[26] Göttlich S., Herty M., Klar A., Network Models for Supply Chains, Commun. Math. Sci. 3 (4) (2005) 545-559. | MR | Zbl

[27] Greenberg J. M., Klar A., Rascle M., Congestion on Multilane Highways, SIAM J. Appl. Math. 63 (3) (2003) 818-833, (electronic). | MR | Zbl

[28] Helbing D., Improved Fluid-Dynamic Model for Vehicular Traffic, Phys. Rev. E 51 (4) (Apr. 1995) 3164-3169.

[29] Helbing D., Traffic and Related Self-Driven Many-Particle Systems, Rev. Modern Phys. 73 (2001) 1067-1141.

[30] Helbing D., Siegmeier J., Lämmer S., Self-Organized Network Flows, Netw. Heterog. Media 2 (2) (2007) 193-210. | MR | Zbl

[31] Herty M., Moutari S., Rascle M., Optimization Criteria for Modelling Intersections of Vehicular Traffic Flow, Netw. Heterog. Media 1 (2) (2006) 193-210. | MR | Zbl

[32] Holden H., Risebro N. H., A Mathematical Model of Traffic Flow on a Network of Unidirectional Roads, SIAM J. Math. Anal. 26 (4) (1995) 999-1017. | MR | Zbl

[33] Holden H., Risebro N. H., Front Tracking for Hyperbolic Conservation Laws, Appl. Math. Sci., vol. 152, Springer-Verlag, New York, 2002. | MR | Zbl

[34] Lighthill M. J., Whitham G. B., On Kinematic Waves. II. a Theory of Traffic Flow on Long Crowded Road, Proc. Roy. Soc. London. Ser. A 229 (1955) 317-345. | MR | Zbl

[35] Marigo A., Piccoli B., A Fluid Dynamic Model for T-Junctions, SIAM J. Math. Anal. 39 (6) (2008) 2016-2032. | MR | Zbl

[36] Payne H. J., Models of Freeway Traffic and Control, in Mathematical Models of Public Systems, Simul. Counc. Proc. 1 (1971).

[37] Richards P. I., Shock Waves on the Highway, Oper. Res. 4 (1956) 42-51. | MR

[38] Siebel F., Mauser W., On the Fundamental Diagram of Traffic Flow, SIAM J. Appl. Math. 66 (4) (2006) 1150-1162, (electronic). | MR | Zbl

[39] Whitham G. B., Linear and Nonlinear Waves, Pure Appl. Math., Wiley-Interscience, John Wiley & Sons, New York, 1974. | MR | Zbl

[40] Zhang H. M., A Non-Equilibrium Traffic Model Devoid of Gas-Like Behavior, Transportation Research Part B 236 (2002) 275-290.

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