Open Access
September 2005 Source-Destination Flow on a Road Network
Mauro Garavello, Benedetto Piccoli
Commun. Math. Sci. 3(3): 261-283 (September 2005).


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 definition 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.


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Mauro Garavello. Benedetto Piccoli. "Source-Destination Flow on a Road Network." Commun. Math. Sci. 3 (3) 261 - 283, September 2005.


Published: September 2005
First available in Project Euclid: 3 October 2005

zbMATH: 1136.90324
MathSciNet: MR2165018

Rights: Copyright © 2005 International Press of Boston

Vol.3 • No. 3 • September 2005
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