This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from the conservation of the number of cars, defined on a road network that is a collection of roads with junctions. The evolution problem is underdetermined at junctions, hence we choose to have some fixed rules for the distribution of traffic plus an optimization criteria for the flux. We prove existence of solutions to the Cauchy problem and we show that the Lipschitz continuous dependence by initial data does not hold. Our method is based on wave front tracking approach, see {[4].}
Garavello, M., Piccoli, B. (2007). A fluidodynamic model for traffic in a road network. In Traffic and granular flow '05 (pp.383-392). Springer [10.1007/978-3-540-47641-2_34].
A fluidodynamic model for traffic in a road network
GARAVELLO, MAURO;
2007
Abstract
This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from the conservation of the number of cars, defined on a road network that is a collection of roads with junctions. The evolution problem is underdetermined at junctions, hence we choose to have some fixed rules for the distribution of traffic plus an optimization criteria for the flux. We prove existence of solutions to the Cauchy problem and we show that the Lipschitz continuous dependence by initial data does not hold. Our method is based on wave front tracking approach, see {[4].}
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