The continuum limit of Follow-the-Leader models — a short proof

Helge Holden; Nils Henrik Risebro

doi:10.3934/dcds.2018031

Article Contents

2018, Volume 38, Issue 2: 715-722. Doi: 10.3934/dcds.2018031

This issue Previous Article Nonlinear Schrödinger Equations on Periodic Metric Graphs Next Article On uniqueness of measure-valued solutions to Liouville's equation of Hamiltonian PDEs

The continuum limit of Follow-the-Leader models — a short proof

Helge Holden^1, , and
Nils Henrik Risebro^2,

1.
Department of Mathematical Sciences, NTNU Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
2.
Department of Mathematics, University of Oslo, Blindern, NO-0316 Oslo, Norway

* Corresponding author: Helge Holden
* Corresponding author: Helge Holden

Received: July 2017

Published: November 2017

Research was supported by the grant Waves and Nonlinear Phenomena (WaNP) from the Research Council of Norway. The research was done while the authors were at Institut MittagLeffler, Stockholm

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Abstract

We offer a simple and self-contained proof that the Follow-the-Leader model converges to the Lighthill-Whitham-Richards model for traffic flow.

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Mathematics Subject Classification: Primary: 35L02; Secondary: 35Q35, 82B21.

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References

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