A non-local macroscopic model for traffic flow

In this work, we propose a non-local Hamilton-Jacobi model for traffic flow and we prove the existence and uniqueness of the solution of this model. This model is justified as the limit of a rescaled microscopic model. We also propose a numerical scheme and we prove an estimate error between the continuous solution of this problem and the numerical one. Finally, we provide some numerical illustrations.

Automated summary

This work introduces a non-local Hamilton-Jacobi model for traffic flow and proves the existence and uniqueness of its solution, as well as a numerical scheme with estimated error. It also presents some numerical illustrations.