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September  2010, 5(3): 565-581. doi: 10.3934/nhm.2010.5.565

A review of conservation laws on networks

Mauro Garavello 1,

1. 

DiSTA, University of Piemonte Orientale "A. Avogadro”, Viale T. Michel 11, 15121 Alessandria, Italy

Received  January 2010 Revised  April 2010 Published  July 2010

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.
Keywords: car traffic, Conservation laws, gas pipeline, telecommunication., networks.
Mathematics Subject Classification: Primary: 35L65; Secondary: 76N10, 90B2.
Citation: Mauro Garavello. A review of conservation laws on networks. Networks & Heterogeneous Media, 2010, 5 (3) : 565-581. doi: 10.3934/nhm.2010.5.565
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