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

TL;DR

This paper establishes the well-posedness of a traffic flow model with non-smooth, non-local interactions and demonstrates convergence of particle methods to approximate solutions, advancing the mathematical understanding of traffic dynamics.

Contribution

It proves existence and uniqueness of solutions for a non-smooth, non-local traffic flow model and introduces a particle method for approximation.

Findings

Existence and uniqueness of solutions established.

Convergence of particle system to the PDE solutions shown.

The model handles discontinuous, anisotropic interactions in traffic flow.

Abstract

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.