In this joint ongoing work with Nicolas Forcadel (INSA Rouen) we study traffic flows models with a bifurcation. The model consists in a single incoming road divided after a junction into several outgoing ones. There are basically two classes of models to describe this situation: microscopic models, which explain how each vehicle behaves  in function of the vehicles in front; and macroscopic ones, taking the form of a conservation law on a junction (or, after integration, a Hamilton-Jacobi equation). Our aim is to derive the macroscopic models from the microscopic ones, thus providing a rigorous justification of the continuous models. The microscopic models being random (in order to take into account the fact that one knows only the distribution of cars taking a given road), the mathematical analysis requires the use of concentration inequalities as well as homogenization type arguments.

https://wp.math.ncsu.edu/nat/ncsu-differential-equations-nonlinear-analysis-seminar-schedule-fall-2021/

Zoom meeting: Link