On the Role of Source Terms in Continuum Traffic Flow Models

We introduce some models for vehicular traffic flow based on hyperbolic balance laws. We focus in particular on source terms for modeling highway entries and exits or local changes of the traffic flow due to inhomogeneities of the road. Rigorous well-posedness results and numerical investigations are presented. We show in particular how real phenomena (e.g. the formation of a queue) that are not captured by models based on systems of conservation laws are instead observable with our models