Entropy solutions for a traffic model with phase transitions

Abstract We introduce an appropriate notion of entropy solution for a generalization of the two phase macroscopic traffic model proposed in Goatin (2006). 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 of the free phase is linearly degenerate, we prove that the obtained weak solutions are in fact entropy solutions. 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.