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.