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

Francesca Marcellini; Francesca Marcellini

doi:10.3934/nhm.2017011

Networks and Heterogeneous Media

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: 01 September 2016 Revised: 01 January 2017
Primary: 35L65; Secondary: 90B20

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.
- Hyperbolic systems of conservation laws,
- continuum traffic models,
- wave-front tracking,
- boundary value problem
Citation: Francesca Marcellini. Existence of solutions to a boundary value problem for a phase transition traffic model[J]. Networks and Heterogeneous Media, 2017, 12(2): 259-275. doi: 10.3934/nhm.2017011

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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.

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