A review of conservation laws on networks

Mauro Garavello; Mauro Garavello

doi:10.3934/nhm.2010.5.565

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

Mauro Garavello ^{1
,}

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.
- Conservation laws,
- networks,
- car traffic,
- gas pipeline,
- telecommunication
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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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.
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