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

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.