A traffic flow model with non-smooth metric interaction: well-posedness and micro-macro limit
Analysis of PDEs
2015-10-16 v1
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 -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.
Keywords
Cite
@article{arxiv.1510.04461,
title = {A traffic flow model with non-smooth metric interaction: well-posedness and micro-macro limit},
author = {Paola Goatin and Francesco Rossi},
journal= {arXiv preprint arXiv:1510.04461},
year = {2015}
}