“A Note on the Entropy Solutions of the Hydrodynamic Model of Traffic Flow” Revisited | Zendy

R. Herbin | Zendy; Ludovic Leclercq | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

“A Note on the Entropy Solutions of the Hydrodynamic Model of Traffic Flow” Revisited

Author(s) -

R. Herbin,

Ludovic Leclercq

Publication year - 2010

Publication title -

transportation science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.965

H-Index - 115

eISSN - 1526-5447

pISSN - 0041-1655

DOI - 10.1287/trsc.1100.0342

Subject(s) - entropy (arrow of time) , mathematics , statistical physics , piecewise , piecewise linear function , flow (mathematics) , mathematical economics , calculus (dental) , mathematical optimization , mathematical analysis , physics , thermodynamics , geometry , medicine , dentistry

This note revisits a paper from Velan and Florian (Velan, S., M. Florian. 2002. A note on the entropy solutions of the hydrodynamic model of traffic flow. Transportation Sci.36(4) 435--446) dealing with the entropy condition in traffic flow models. It aims to clarify the application of this condition for nondifferentiable fundamental diagrams and then to correct some misunderstandings that appear in the above-mentioned paper. This note clearly exhibits that the nonsmoothness of the fundamental diagram does not change the properties of the Lighthill-Whitham-Richards (LWR) solutions: (i) existence of a unique entropy solution and (ii) nonuniqueness of weak solutions. These precisions are important because piecewise linear fundamental diagrams appear to accurately fit with experimental observations and cannot be disproved on an alleged mathematical basis.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research