Measure-valued solutions to nonlocal transport equations on networks

Aiming to describe traffic flow on road networks with long-range driver interactions, we study a nonlinear transport equation defined on an oriented network where the velocity field depends not only on the state variable but also on the distribution of the population. We prove existence, uniqueness and continuous dependence results of the solution intended in a suitable measure-theoretic sense. We also provide a representation formula in terms of the push-forward of the initial and boundary data along the network and discuss an explicit example of nonlocal velocity field fitting our framework.