Continuous Riemann solvers for traffic flow at a junction
Alberto Bressan and Fang Yu
Abstract: The paper studies a class of conservation law models for traffic flow on a family of roads, near a junction. A Riemann Solver is constructed, where the incoming and outgoing fluxes depend Hölder continuously on the traffic density and on the drivers’ turning preferences. On the other hand, it is proved that no Lipschitz continuous Riemann Solver can exist, satisfying natural modeling assumptions. Various examples show that, if junction conditions are assigned in terms of Riemann Solvers, then the Cauchy problem on a network of roads is ill posed, even for initial data having small total variation.