On the stability of the improved Aw-Rascle-Zhang model with Chaplygin pressure

In this paper, we mainly study the stability of Riemann problem for the improved Aw-Rascle-Zhang model which describes the formation and dynamics of traffic jams. First of all, we construct the classical Riemann solutions by elementary waves with the method of characteristic analysis. With the generalized Rankine-Hugoniot and entropy conditions, we prove the existence and uniqueness of delta-shock wave for arbitrary convex F(u) in this model. Then through a small perturbation, we analyze the wave interactions of different kinds of waves. As a result, we get the stability for the Riemann problem by letting the perturbed parameter epsilon -> 0. (C) 2021 Elsevier Ltd. All rights reserved.

Automated summary

This paper investigates the stability of the Riemann problem for the improved Aw-Rascle-Zhang model, which describes the formation and dynamics of traffic jams. By constructing classical Riemann solutions and analyzing wave interactions, the existence and uniqueness of delta-shock wave in this model are proven, leading to stability analysis of the Riemann problem.