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

This note revisits a paper from Velan and Florian [Velan and Florian(2002)] dealing with the entropy condition in traffic flow models. It aims to clarify the application of this condition for non-differentiable fundamental diagrams and then to correct some misunderstandings that appear in the above-mentioned paper. Notably, this note clearly exhibits that the non-smoothness of the fundamental diagram does not change the properties of the LWR solutions: (i) existence of a unique entropy solution and (ii) non-uniqueness 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.