On a class of nonlocal traffic flow models with multivalued fundamental diagram

Thomas Lorenz
RheinMain University of Applied Sciences

Many PDE models for traffic flow have the continuity equation in common and then differ from each other in the choice of the fundamental diagram. In this talk, a broad class of multiscale models is considered from the analytical point of view. Their systems consist of square integrable solutions and Radon measure-valued solutions to transport equations with nonlocal dependences. Since fundamental diagrams are very difficult to detect precisely, it is preferred to talk more than one flux function into consideration simultaneously. This leads to a form of differential inclusions and, all this can be handled in a joint metric setting.

Presentation (PDF File)

Back to Workshop I: Mathematical Foundations of Traffic