带有Chaplygin压力的耦合Aw-Rascle模型黎曼解的极限  

The Limits of the Riemann Solutions to the Coupled Aw-Rascle Model with the Chaplygin Pressure

作　　者：翁莎莎 潘丽君 吕顺 WENG Shasha;PAN Lijun;LYU Shun(School of Mathematics,Nanjing University of Aeronautics and Astronautics,Nanjing Jiangsu 211106,China;Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA),Ministry of Industry and Information Technology,Nanjing Jiangsu 211106,China)

机构地区：[1]南京航空航天大学数学学院,江苏南京211106 [2]工业和信息化部飞行器数学建模和高性能计算重点实验室(NUAA),江苏南京211106

出　　处：《新疆大学学报（自然科学版）（中英文）》2023年第6期683-690,共8页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：中央高校基本科研业务费专项资金“非线性双守恒律中的高维燃烧问题”(NZ2014107)。

摘　　要：研究了带有Chaplygin压力的耦合Aw-Rascle(CAR)交通模型的黎曼问题.通过令耦合模型两侧压力同时消失,得到上述黎曼解的极限,并证明了该极限具有相同初值的无压气体动力(Pressureless Gas Dynamics,PGD)模型的黎曼解.更进一步,证得极限后的delta激波解的权重和速度与PGD模型的delta激波解的权重和速度完全一致.此外,由解的渐近行为,可以观察到稀疏接触间断到接触间断的转化.This paper considers the Riemann problem of the coupled Aw-Rascle(CAR)model with Chaplygin pressure.By letting the pressures on both sides of the CAR model vanish,the limits of the above Riemann solutions are obtained.Moreover,it is proved that the limits are the Riemann solutions to the pressureless gas dynamics(PGD)model with the same initial value.The weight and velocity of the delta shock after the limit are completely consistent with the weight and velocity of the delta shock to the PGD model.Furthermore,from the asymptotic behavior of the solutions,the transition from the rarefactive contact discontinuity to the contact discontinuity can be observed.

关 键 词：耦合Aw-Rascle模型 无压气体动力模型 Chaplygin压力 delta激波 极限解 

分 类 号：O175.2[理学—数学]