Traffic flow models with phase transitions on road networks

  • Received: 01 September 2008 Revised: 01 December 2008
  • 90B20, 35L65.

  • The paper presents a review of the main analytical results available on the traffic flow model with phase transitions described in [10]. We also introduce a forthcoming existence result on road networks [14].

    Citation: Paola Goatin. Traffic flow models with phase transitions on road networks[J]. Networks and Heterogeneous Media, 2009, 4(2): 287-301. doi: 10.3934/nhm.2009.4.287

    Related Papers:

    [1] Mohamed Benyahia, Massimiliano D. Rosini . A macroscopic traffic model with phase transitions and local point constraints on the flow. Networks and Heterogeneous Media, 2017, 12(2): 297-317. doi: 10.3934/nhm.2017013
    [2] Paola Goatin . Traffic flow models with phase transitions on road networks. Networks and Heterogeneous Media, 2009, 4(2): 287-301. doi: 10.3934/nhm.2009.4.287
    [3] Maya Briani, Emiliano Cristiani . An easy-to-use algorithm for simulating traffic flow on networks: Theoretical study. Networks and Heterogeneous Media, 2014, 9(3): 519-552. doi: 10.3934/nhm.2014.9.519
    [4] Frederike Kissling, Christian Rohde . The computation of nonclassical shock waves with a heterogeneous multiscale method. Networks and Heterogeneous Media, 2010, 5(3): 661-674. doi: 10.3934/nhm.2010.5.661
    [5] Mauro Garavello, Roberto Natalini, Benedetto Piccoli, Andrea Terracina . Conservation laws with discontinuous flux. Networks and Heterogeneous Media, 2007, 2(1): 159-179. doi: 10.3934/nhm.2007.2.159
    [6] Francesca Marcellini . Existence of solutions to a boundary value problem for a phase transition traffic model. Networks and Heterogeneous Media, 2017, 12(2): 259-275. doi: 10.3934/nhm.2017011
    [7] Michael Herty, Niklas Kolbe, Siegfried Müller . Central schemes for networked scalar conservation laws. Networks and Heterogeneous Media, 2023, 18(1): 310-340. doi: 10.3934/nhm.2023012
    [8] Alberto Bressan, Khai T. Nguyen . Conservation law models for traffic flow on a network of roads. Networks and Heterogeneous Media, 2015, 10(2): 255-293. doi: 10.3934/nhm.2015.10.255
    [9] Simone Göttlich, Camill Harter . A weakly coupled model of differential equations for thief tracking. Networks and Heterogeneous Media, 2016, 11(3): 447-469. doi: 10.3934/nhm.2016004
    [10] Benjamin Seibold, Morris R. Flynn, Aslan R. Kasimov, Rodolfo R. Rosales . Constructing set-valued fundamental diagrams from Jamiton solutions in second order traffic models. Networks and Heterogeneous Media, 2013, 8(3): 745-772. doi: 10.3934/nhm.2013.8.745
  • The paper presents a review of the main analytical results available on the traffic flow model with phase transitions described in [10]. We also introduce a forthcoming existence result on road networks [14].


  • This article has been cited by:

    1. Mohamed Benyahia, Massimiliano D. Rosini, A macroscopic traffic model with phase transitions and local point constraints on the flow, 2017, 12, 1556-181X, 297, 10.3934/nhm.2017013
    2. MAURO GARAVELLO, BENEDETTO PICCOLI, COUPLING OF LIGHTHILL–WHITHAM–RICHARDS AND PHASE TRANSITION MODELS, 2013, 10, 0219-8916, 577, 10.1142/S0219891613500215
    3. Zlatinka Dimitrova, Flows of Substances in Networks and Network Channels: Selected Results and Applications, 2022, 24, 1099-4300, 1485, 10.3390/e24101485
  • Reader Comments
  • © 2009 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(4016) PDF downloads(92) Cited by(3)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog