Existence of solutions for the Aw–Rascle traffic flow model with vacuum
Marte Godvik and Harald Hanche-Olsen
Abstract: We consider the macroscopic model for traffic flow proposed by Aw and Rascle in [doi:10.1137/S0036139997332099]. 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 us unable to control the total variation of the conservative variables. We allow vacuum to appear and prove existence of a weak entropy solution to the Cauchy problem.