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

Francesca Marcellini

doi:10.3934/nhm.2017011

Article Contents

2017, Volume 12, Issue 2: 259-275. Doi: 10.3934/nhm.2017011

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

Francesca Marcellini

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

Received: August 31, 2016

Revised: December 31, 2016

Published: October 2017

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Abstract

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.

Keywords:

Hyperbolic systems of conservation laws,
continuum traffic models,
wave-front tracking,
boundary value problem.

Mathematics Subject Classification: Primary: 35L65; Secondary: 90B20.

Citation:

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Figure 1. The free phase $F$ and the congested phase $C$ resulting from (1.1) in the coordinates, from left to right, $(\rho,\eta)$ and $(\rho, \rho v)$

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Figure 2. 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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References

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