Conservation laws on complex networks

Mauro Garavello; Benedetto Piccoli

Annales de l'I.H.P. Analyse non linéaire (2009)

  • Volume: 26, Issue: 5, page 1925-1951
  • ISSN: 0294-1449

How to cite

top

Garavello, Mauro, and Piccoli, Benedetto. "Conservation laws on complex networks." Annales de l'I.H.P. Analyse non linéaire 26.5 (2009): 1925-1951. <http://eudml.org/doc/78919>.

@article{Garavello2009,
author = {Garavello, Mauro, Piccoli, Benedetto},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {traffic flow; wave-front tracking; Lighthill-Whitham-Richards method; Lipschitz continuous dependence},
language = {eng},
number = {5},
pages = {1925-1951},
publisher = {Elsevier},
title = {Conservation laws on complex networks},
url = {http://eudml.org/doc/78919},
volume = {26},
year = {2009},
}

TY - JOUR
AU - Garavello, Mauro
AU - Piccoli, Benedetto
TI - Conservation laws on complex networks
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2009
PB - Elsevier
VL - 26
IS - 5
SP - 1925
EP - 1951
LA - eng
KW - traffic flow; wave-front tracking; Lighthill-Whitham-Richards method; Lipschitz continuous dependence
UR - http://eudml.org/doc/78919
ER -

References

top
  1. [1] Aw A., Rascle M., Resurrection of “second order” models of traffic flow, SIAM J. Appl. Math.60 (3) (2000) 916-938, (electronic). Zbl0957.35086MR1750085
  2. [2] Banda M.K., Herty M., Klar A., Gas flow in pipeline networks, Netw. Heterog. Media1 (1) (2006) 41-56. Zbl1108.76063MR2219276
  3. [3] Bardos C., Le Roux A.Y., Nédélec J.C., First order quasilinear equations with boundary conditions, Comm. Partial Differential Equations4 (1979) 1017-1034. Zbl0418.35024MR542510
  4. [4] Bastin G., Haut B., A second order model of arc junctions in fluid models of traffic networks, Netw. Heterog. Media2 (2) (2007) 227-253. Zbl1161.35443MR2291820
  5. [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. Media2 (4) (2007) 569-595. Zbl1143.90006MR2357759
  6. [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. Mecanique333 (2005) 843-851. Zbl1177.90076
  7. [7] Benzoni-Gavage S., Colombo R.M., An n-populations model for traffic flow, European J. Appl. Math.14 (5) (2003) 587-612. Zbl1143.82323MR2020123
  8. [8] Bressan A., A contractive metric for systems of conservation laws with coinciding shock and rarefaction curves, J. Differential Equations106 (1993) 332-366. Zbl0802.35095MR1251857
  9. [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. Zbl0997.35002MR1816648
  10. [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. Zbl0958.35001MR1686652
  11. [11] Chitour Y., Piccoli B., Traffic circles timing of traffic lights for cars flow, Discrete Contin. Dyn. Syst. Ser. B5 (3) (2005) 599-630. Zbl1086.35066MR2151724
  12. [12] Coclite G.M., Garavello M., Piccoli B., Traffic flow on a road network, SIAM J. Math. Anal.36 (6) (2005) 1862-1886. Zbl1114.90010MR2178224
  13. [13] Colombo R.M., Hyperbolic phase transitions in traffic flow, SIAM J. Appl. Math.63 (2) (2002) 708-721, (electronic). Zbl1037.35043MR1951956
  14. [14] Colombo R.M., Garavello M., A well posed Riemann problem for the p-system at a junction, Netw. Heterog. Media1 (3) (2006) 495-511. Zbl1116.35086MR2247787
  15. [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. Zbl1155.35399MR2377285
  16. [16] R.M. Colombo, P. Goatin, B. Piccoli, Road network with phase transitions, preprint. 
  17. [17] Dafermos C.M., Hyperbolic Conservation Laws in Continuum Physics, Grundlehren Math. Wiss., vol. 325, second ed., Springer-Verlag, Berlin, 2005. Zbl1078.35001MR2169977
  18. [18] D'apice C., Manzo R., A fluid dynamic model for supply chains, Netw. Heterog. Media1 (3) (2006) 379-398. Zbl1131.90002MR2247783
  19. [19] D'apice C., Manzo R., Piccoli B., Packet flow on telecommunication networks, SIAM J. Math. Anal.38 (3) (2006) 717-740, (electronic). Zbl1147.35331MR2262939
  20. [20] Dubois F., LeFloch P., Boundary conditions for nonlinear hyperbolic systems of conservation laws, J. Differential Equations71 (1) (1988) 93-122. Zbl0649.35057MR922200
  21. [21] Garavello M., Natalini R., Piccoli B., Terracina A., Conservation laws with discontinuous flux, Netw. Heterog. Media2 (1) (2007) 159-179, (electronic). Zbl1142.35511MR2291816
  22. [22] Garavello M., Piccoli B., Source-destination flow on a road network, Commun. Math. Sci.3 (3) (2005) 261-283. Zbl1136.90324MR2165018
  23. [23] Garavello M., Piccoli B., Traffic flow on a road network using the Aw–Rascle model, Comm. Partial Differential Equations31 (1–3) (2006) 243-275. Zbl1090.90032MR2209753
  24. [24] Garavello M., Piccoli B., Traffic Flow on Networks, AIMS Ser. Appl. Math., vol. 1, AIMS, 2006. Zbl1136.90012MR2328174
  25. [25] Goatin P., The Aw–Rascle vehicular traffic flow model with phase transitions, Math. Comput. Modelling44 (3–4) (2006) 287-303. Zbl1134.35379MR2239057
  26. [26] Göttlich S., Herty M., Klar A., Network models for supply chains, Commun. Math. Sci.3 (4) (2005) 545-559. Zbl1115.90008MR2188683
  27. [27] Greenberg J.M., Klar A., Rascle M., Congestion on multilane highways, SIAM J. Appl. Math.63 (3) (2003) 818-833, (electronic). Zbl1024.35064MR1969676
  28. [28] Helbing D., Improved fluid-dynamic model for vehicular traffic, Phys. Rev. E51 (4) (Apr. 1995) 3164-3169. 
  29. [29] Helbing D., Traffic and related self-driven many-particle systems, Rev. Modern Phys.73 (2001) 1067-1141. 
  30. [30] Helbing D., Siegmeier J., Lämmer S., Self-organized network flows, Netw. Heterog. Media2 (2) (2007) 193-210. Zbl1160.90344MR2291818
  31. [31] Herty M., Moutari S., Rascle M., Optimization criteria for modelling intersections of vehicular traffic flow, Netw. Heterog. Media1 (2) (2006) 193-210. Zbl1131.90016MR2223072
  32. [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. Zbl0833.35089MR1338371
  33. [33] Holden H., Risebro N.H., Front Tracking for Hyperbolic Conservation Laws, Appl. Math. Sci., vol. 152, Springer-Verlag, New York, 2002. Zbl1006.35002MR1912206
  34. [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. A229 (1955) 317-345. Zbl0064.20906MR72606
  35. [35] Marigo A., Piccoli B., A fluid dynamic model for T-junctions, SIAM J. Math. Anal.39 (6) (2008) 2016-2032. Zbl1153.90004MR2390323
  36. [36] Payne H.J., Models of freeway traffic and control, in mathematical models of public systems, Simul. Counc. Proc.1 (1971). 
  37. [37] Richards P.I., Shock waves on the highway, Oper. Res.4 (1956) 42-51. MR75522
  38. [38] Siebel F., Mauser W., On the fundamental diagram of traffic flow, SIAM J. Appl. Math.66 (4) (2006) 1150-1162, (electronic). Zbl1102.35068MR2246050
  39. [39] Whitham G.B., Linear and Nonlinear Waves, Pure Appl. Math., Wiley–Interscience, John Wiley & Sons, New York, 1974. Zbl0373.76001MR483954
  40. [40] Zhang H.M., A non-equilibrium traffic model devoid of gas-like behavior, Transportation Research Part B236 (2002) 275-290. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.