A General Phase Transition Model for Vehicular Traffic

This paper provides a mathematical model of the phenomenon of phase transitions in traffic flow. The model consists of a scalar conservation law coupled with a 2 × 2 system of conservation laws. The coupling is achieved via a free boundary, where the phase transition takes place. For this model, the Riemann problem is stated and globally solved. The Cauchy problem is proved to admit a solution defined globally in time without any assumption about the smallness of the initial data or the number of phase boundaries. Qualitative properties of real traffic flow are shown to agree with properties of the solutions of the model.