耦合Aw-Rascle-Zhang模型的Riemann解及其稳定性  

Riemann Solution and Stability of Coupled Aw-Rascle-Zhang Model

作　　者：潘丽君 吕顺 翁莎莎 Pan Lijun;Lv Shun;Weng Shasha(School of Mathematics,Nanjing University of Aeronautics and Astronautics,Nanjing 211106;Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA),MIIT,Nanjing 211106)

机构地区：[1]南京航空航天大学数学学院,南京211106 [2]航空飞行器数学建模与高性能计算重点实验室,南京211106

出　　处：《数学物理学报（A辑）》2024年第4期885-895,共11页Acta Mathematica Scientia

基　　金：中国留学基金(201506835005)。

摘　　要：该文主要研究在单连通道路上具有不同压力项的耦合Aw-Rascle-Zhang(CARZ)交通流模型的黎曼问题,利用特征分析法和相变的相关理论,构造了文献[5]缺失的情形v−+η(ρ−)^(γ)=v+的稳定显式解,并修正了情形v++η(ρ−)γ<v+的黎曼解,完善了Herty[5]等人的工作.当CARZ模型中压力项前面的参数μ→η时,证明了该模型黎曼解的唯一性和稳定性.This paper studies the Riemann problem of the coupled Aw-Rascle-Zhang traffic model with different pressure laws on the connected roads.Using the method of characteristic analysis and theories of phase transition,we construct the Riemann solution to the coupled Aw-Rascle-Zhang model for the ommitted case v−+η(ρ−)^(γ)=v+in reference[5],and correct Riemann solution for the case v++η(ρ−)γ<v+,which complete the work of Herty,et al.Furthermore,when the parameter of the pressure termμ→η,the uniqueness and stability of the Riemann solution of the coupled Aw-Rascle model are proved.

关 键 词：耦合Aw-Rascle-Zhang交通流模型 黎曼问题 唯一性 稳定性 

分 类 号：O175.27[理学—数学]