Communications in Mathematical Sciences

Volume 15 (2017)

Number 1

A traffic flow model with non-smooth metric interaction: Well-posedness and micro-macro limit

Pages: 261 – 287



Paola Goatin (Inria Sophia Antipolis Méditerranée, Sophia Antipolis, France)

Francesco Rossi (Laboratoire des Sciences de l’Information et des Systèmes, Aix Marseille Université, Marseille, France)


We prove existence and uniqueness of solutions to a transport equation modelling vehicular traffic in which the velocity field depends non-locally on the downstream traffic density via a discontinuous anisotropic kernel. The result is obtained recasting the problem in the space of probability measures equipped with the $\infty$-Wasserstein distance. We also show convergence of solutions of a finite dimensional system, which provide a particle method to approximate the solutions to the original problem.


transport equations, non-local velocity, Wasserstein distance, macroscopic traffic flow models, micro-macro limits

2010 Mathematics Subject Classification

Primary 35F25, 35L65. Secondary 65M12, 90B20.

Published 10 January 2017