American Institute of Mathematical Sciences

June  2017, 12(2): 259-275. doi: 10.3934/nhm.2017011

Existence of solutions to a boundary value problem for a phase transition traffic model

 Dipartimento di Matematica e Applicazioni, Università di Milano Bicocca, via R. Cozzi 55, 20125 Milano, Italy

Received  September 2016 Revised  January 2017 Published  May 2017

We consider the initial boundary value problem for the phase transition traffic model introduced in [9], which is a macroscopic model based on a 2×2 system of conservation laws. We prove existence of solutions by means of the wave-front tracking technique, provided the initial data and the boundary conditions have finite total variation.

Citation: Francesca Marcellini. Existence of solutions to a boundary value problem for a phase transition traffic model. Networks & Heterogeneous Media, 2017, 12 (2) : 259-275. doi: 10.3934/nhm.2017011
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References:
The free phase $F$ and the congested phase $C$ resulting from (1.1) in the coordinates, from left to right, $(\rho,\eta)$ and $(\rho, \rho v)$
Wave interactions in a road. Above, from left to right, the cases $2-1/1-2$ and $\mathcal{LW}-\mathcal{PT}/\mathcal{PT}-2$. Below, from left to right, the cases $1-1/1$ and $\mathcal{PT}-1/\mathcal{PT}$
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