Networks and Heterogeneous Media (NHM)

A review of conservation laws on networks

Pages: 565 - 581, Volume 5, Issue 3, September 2010      doi:10.3934/nhm.2010.5.565

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Mauro Garavello - DiSTA, University of Piemonte Orientale "A. Avogadroā€¯, Viale T. Michel 11, 15121 Alessandria, Italy (email)

Abstract: 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:  Conservation laws, networks, car traffic, gas pipeline, telecommunication.
Mathematics Subject Classification:  Primary: 35L65; Secondary: 76N10, 90B20.

Received: January 2010;      Revised: April 2010;      Available Online: July 2010.