Journal
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
Volume 62, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.nonrwa.2021.103351
Keywords
Conservation laws; Riemann problem; Improved Aw-Rascle-Zhang model; delta-shock wave; Wave interaction; Traffic flow
Categories
Funding
- Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan), China [CUGL180827]
- Natural Science Foundation of Zhejiang, China [LQ18A010004]
- WenZhou Municipal Science and Technology Bureau, China [2020G0038]
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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.
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.
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