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.

Garavello, M. (2010). A review of conservation laws on networks. NETWORKS AND HETEROGENEOUS MEDIA, 5(3), 565-581 [10.3934/nhm.2010.5.565].

A review of conservation laws on networks

GARAVELLO, MAURO
2010

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.
Articolo in rivista - Articolo scientifico
VEHICULAR TRAFFIC FLOW; P-SYSTEM; PHASE-TRANSITIONS; 2ND-ORDER MODELS; SUPPLY CHAINS; ROAD NETWORK; JUNCTION; OPTIMIZATION; WAVES
English
2010
5
3
565
581
none
Garavello, M. (2010). A review of conservation laws on networks. NETWORKS AND HETEROGENEOUS MEDIA, 5(3), 565-581 [10.3934/nhm.2010.5.565].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/37052
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