Conservation laws with nonlocality in density and velocity and their applicability in traffic flow modelling
Analysis of PDEs
2023-04-25 v2
Abstract
In this work we present a nonlocal conservation law with a velocity depending on an integral term over a part of the space. The model class covers already existing models in literature, but it is also able to describe new dynamics mainly arising in the context of traffic flow modelling. We prove the existence and uniqueness of weak solutions of the nonlocal conservation law. Further, we provide a suitable numerical discretization and present numerical examples.
Keywords
Cite
@article{arxiv.2302.12797,
title = {Conservation laws with nonlocality in density and velocity and their applicability in traffic flow modelling},
author = {Jan Friedrich and Simone Göttlich and Alexander Keimer and Lukas Pflug},
journal= {arXiv preprint arXiv:2302.12797},
year = {2023}
}