Existence of Solutions for the Aw–rascle Traffic Flow Model With Vacuum

In this paper, the macroscopic model for traffic flow proposed by Aw and Rascle in 2000 is considered. The model is a 2 × 2 system of hyperbolic conservation laws, or, when the model includes a relaxation term, a 2 × 2 system of hyperbolic balance laws. The main difficulty is the presence of vacuum, which makes control of the total variation of the conservative variables impossible. We allow vacuum to appear and prove the existence of a weak entropy solution to the Cauchy problem.