关键词: AR交通模型, 黎曼解, 广义R-H条件, Delta激波, Chaplygin压力, 熵条件

Abstract: The Riemann problem for the Aw-Rascle (AR) traffic model with generalized Chaplygin 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 constructed, and the generalized Rankine-Hugoniot conditions and the δ-entropy condition are clarified. In particular, the existence and uniqueness of δ-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.

Key words: Aw-Rascle traffic model, Generalized Chaplygin pressure, Riemann problem, Generalized Rankine-Hugoniot relation, Delta shock wave, Entropy condition