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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.