Continuous Riemann solvers  for traffic flow  at a junction

Alberto Bressan; Fang Yu

doi:10.3934/dcds.2015.35.4149

Article Contents

2015, Volume 35, Issue 9: 4149-4171. Doi: 10.3934/dcds.2015.35.4149

This issue Previous Article Local properties of almost-Riemannian structures in dimension 3 Next Article A model problem for Mean Field Games on networks

Continuous Riemann solvers for traffic flow at a junction

Alberto Bressan^1, and
Fang Yu^2,

1.
Department of Mathematics, Penn State University, University Park, Pa.16802
2.
Department of Mathematics, Penn State University, University Park, PA. 16802

Received: May 2014

Revised: August 2014

Published: May 2017

Abstract / Introduction Related Papers Cited by

Abstract

The paper studies a class of conservation law models for traffic flow on a family of roads, near a junction. A Riemann Solver is constructed, where the incoming and outgoing fluxes depend Hölder continuously on the traffic density and on the drivers' turning preferences. However, various examples show that, if junction conditions are assigned in terms of Riemann Solvers, then the Cauchy problem on a network of roads can be ill posed, even for initial data having small total variation.

Keywords:

Mathematics Subject Classification: Primary: 35Q93, 35L65; Secondary: 90B20.

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References

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