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

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.