Conservation laws with nonlocality in density and velocity and their applicability in traffic flow modelling

TL;DR

This paper introduces a nonlocal conservation law with velocity depending on an integral over space, applicable to traffic flow modeling, and provides theoretical proofs and numerical methods for its solutions.

Contribution

It presents a new nonlocal conservation law model, proves existence and uniqueness of solutions, and offers numerical discretization for traffic flow applications.

Findings

Model covers existing and new traffic dynamics

Proves existence and uniqueness of solutions

Provides numerical discretization and examples

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.