“Micro-Macro Limit: From the Follow-the-Leader Model to the Lighthill-Whitham-Richards Model”
Wednesday 1 March 2023 h. 15:30 - Room 2BC30 - Mohamed Bentaibi (Padova, Dip. Mat.)
The Lighthill-Whitham-Richards (LWR) model is a hyperbolic conservation law where the solution is a macroscopic density that typically represents the average spatial concentration of vehicles. The Follow-the-Leader model (FtL) instead can be thought as a dynamical system of N cars in which each car travels with a velocity that depends on its relative distance with respect to the car immediately in front. With the FtL model we build a microscopic density which approximates the macroscopic one. After briefly introducing both the LWR and the FtL models, we prove that the microscopic density converges to the macroscopic one in a suitable topology. We also present new results regarding the microscopic stability of the FtL model and its applications to the analysis of the micro-macro limit problem.