压力消失时具有广义Chaplygin气体的Aw-Rascle交通模型Riemann解的极限

Vanishing Pressure Limit of Riemann Solutions to the Aw-Rascle Model for Generalized Chaplygin Gas

该文研究带有广义Chaplygin气体的Aw-Rascle(AR)交通模型的黎曼问题.在广义Rankine-Hugoniot条件和熵条件下,证明了Delta激波存在唯一性.Delta激波有助于描述严重的交通拥堵.更重要的是,证实了广义Chaplygin气体的Aw-Rascle交通模型的黎曼解在交通压力消失时收敛于带相同的初值无压气体动力学系统的黎曼解.

The Riemann problem for the Aw-Rascle （AR） traffic model with generalized Chap- lygin gas is considered. Its first eigenvalue is genuinely nonlinear and the second eigenvalue is linearly degenerate, but the nonclassical solutions appear. The Riemann solutions are con- structed, and the generalized Rankine-Hugoniot conditions and the ^-entropy condition are clarified. In particular, the existence and uniqueness of （^-shock waves are established under the generalized Rankine-Hugoniot conditions and entropy condition. The delta shock may be useful for description of the serious traffic jam. More importantly, it is proved that the limits of the Riemann solutions of the above AR traffic model are exactly those of the pressureless gas dynamics system with the same Riemann initial data as the traffic pressure vanishes.