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Networks and Heterogeneous Media

2010, Volume 5, Issue 3: 565-581. doi: 10.3934/nhm.2010.5.565
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A review of conservation laws on networks

  • 1.
    DiSTA, University of Piemonte Orientale "A. Avogadro”, Viale T. Michel 11, 15121 Alessandria
  • Received: 01 January 2010 Revised: 01 April 2010

  • Primary: 35L65; Secondary: 76N10, 90B20.

  • This paper deals with various applications of conservation laws on networks. In particular we consider the car traffic, described by the Lighthill-Whitham-Richards model and by the Aw-Rascle-Zhang model, the telecommunication case, by using the model introduced by D'Apice-Manzo-Piccoli and, finally, the case of a gas pipeline, modeled by the classical p-system. For each of these models we present a review of some results about Riemann and Cauchy problems in the case of a network, formed by a single vertex with n incoming and m outgoing arcs.

    Citation: Mauro Garavello. A review of conservation laws on networks[J]. Networks and Heterogeneous Media, 2010, 5(3): 565-581. doi: 10.3934/nhm.2010.5.565

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  • This paper deals with various applications of conservation laws on networks. In particular we consider the car traffic, described by the Lighthill-Whitham-Richards model and by the Aw-Rascle-Zhang model, the telecommunication case, by using the model introduced by D'Apice-Manzo-Piccoli and, finally, the case of a gas pipeline, modeled by the classical p-system. For each of these models we present a review of some results about Riemann and Cauchy problems in the case of a network, formed by a single vertex with n incoming and m outgoing arcs.


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  • © 2010 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)
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