Entropy solutions for a traffic model with phase transitions
Provides theoretical foundations for a macroscopic traffic model with phase transitions, but the result is incremental as it extends existing methods to a specific model.
The paper proves existence and a priori bounds for weak solutions of a two-phase traffic model using wave-front tracking, and shows that these solutions are entropy solutions when the free phase is linearly degenerate. A numerical example illustrates qualitative features.
In this paper, we consider the two phases macroscopic traffic model introduced in [P. Goatin, The Aw-Rascle vehicular traffic flow with phase transitions, Mathematical and Computer Modeling 44 (2006) 287-303]. We first apply the wave-front tracking method to prove existence and a priori bounds for weak solutions. Then, in the case the characteristic field corresponding to the free phase is linearly degenerate, we prove that the obtained weak solutions are in fact entropy solutions à la Kruzhkov. The case of solutions attaining values at the vacuum is considered. We also present an explicit numerical example to describe some qualitative features of the solutions.