We construct a model of traffic flow with sources and destinations on a roads network. The model is based on a conservation law for the density of traffic and on semilinear equations for traffic-type functions, i.e. functions describing paths for cars. We propose a deffinition of solution at junctions, which depends on the traffic-type functions. Finally we prove, for every positive time T, existence of entropic solutions on the whole network for perturbations of constant initial data. Our method is based on the wave-front tracking approach.

Garavello, M., Piccoli, B. (2005). Source-destination flow on a road network. COMMUNICATIONS IN MATHEMATICAL SCIENCES, 3(3), 261-283 [10.4310/CMS.2005.v3.n3.a1].

Source-destination flow on a road network

GARAVELLO, MAURO
;
2005

Abstract

We construct a model of traffic flow with sources and destinations on a roads network. The model is based on a conservation law for the density of traffic and on semilinear equations for traffic-type functions, i.e. functions describing paths for cars. We propose a deffinition of solution at junctions, which depends on the traffic-type functions. Finally we prove, for every positive time T, existence of entropic solutions on the whole network for perturbations of constant initial data. Our method is based on the wave-front tracking approach.
Articolo in rivista - Articolo scientifico
Scalar conservation law; Semilinear equation; Traffic flow;
English
2005
3
3
261
283
none
Garavello, M., Piccoli, B. (2005). Source-destination flow on a road network. COMMUNICATIONS IN MATHEMATICAL SCIENCES, 3(3), 261-283 [10.4310/CMS.2005.v3.n3.a1].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/37073
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