The generalized Riemann problem for the Aw–Rascle model with phase transitions

It is proved that the generalized Riemann problem for the Aw–Rascle vehicular traffic flow with phase transitions admits a unique local solution in the class of piecewise C1 functions and in a neighborhood of the origin this solution possesses a structure similar to the solution of the corresponding Riemann problem. Especially, when the vacuum state is involved, the Riemann solution is also well-posed, which allows us to fit experimental data well.