带有时变源项的Chaplygin气体Aw-Rascle交通流模型的阴影波解

Shadow Wave Solution for the Chaplygin Gas Aw-Rascle Traffic Flow Model with Time-Dependent Source Term

摘要: 研究带有时变源项的Chaplygin气体Aw-Rascle交通流模型的阴影波解。由于源项具有时变性，系统失去自相似性，波结构较齐次及常系数情形更为复杂，对阴影波方法的适用性提出了新的要求。本文构造了该模型的超压缩阴影波解，利用超压缩条件建立了其弱唯一性，并证明该解在分布意义下收敛于系统自身的狄拉克激波解。该结果为时变源项作用下交通流中奇异波的形成提供了理论依据，同时拓展了阴影波方法在非齐次系统中的应用范围。

Abstract: This paper investigates the shadow wave solution for the Chaplygin gas Aw-Rascle traffic flow model with a time-dependent source term. Due to the time dependence of the source term, the system loses self-similarity and the wave structure becomes more complex than in the homogeneous and constant-coefficient source cases, which poses new challenges for the applicability of the shadow wave method. In this work, we construct the overcompressive shadow wave solution for this model, establish its weak uniqueness under the overcompressibility condition, and prove that this solution converges to the delta-shock wave solution of the system itself in the distributional sense. The results provide a theoretical foundation for the formation of singular waves in traffic flows under time-dependent source terms, and also extend the applicability of the shadow wave method to nonhomogeneous hyperbolic conservation law systems.