关键词: 耦合 Aw-Rascle-Zhang 交通流模型, 黎曼问题, 唯一性, 稳定性

Abstract:

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_- + \eta (\rho_-)^{\gamma} = v_+ $ in reference [5], and correct Riemann solution for the case $ v_+ + \eta(\rho_-)^{\gamma} < v_+ $, which complete the work of Herty, et al. Furthermore, when the parameter of the pressure term $ \mu \to \eta $, the uniqueness and stability of the Riemann solution of the coupled Aw-Rascle model are proved.

Key words: Coupled Aw-Rascle-Zhang model, Riemann problem, Uniqueness, Stability