Geometric singular perturbation approach to the existence and instability of stationary waves for viscous traffic flow models

John M. Hong, Cheng Hsiung Hsu, Bo Chih Huang, Tzi Sheng Yang

研究成果: 雜誌貢獻期刊論文同行評審

5 引文 斯高帕斯(Scopus)

摘要

The purpose of this work is to study the existence and stability of stationary waves for viscous traffic flow models. From the viewpoint of dynamical systems, the steady-state problem of the systems can be formulated as a singularly perturbed problem. Using the geometric singular perturbation method, we establish the existence of stationary waves for both the inviscid and viscous systems. The inviscid stationary waves contain smooth waves and discontinuous transonic waves. Both waves admit viscous profiles for the viscous systems. Then we consider the linearized eigenvalue problem of the systems along smooth stationary waves. Applying the technique of center manifold reduction, we show that any one of the supersonic smooth stationary waves is spectrally unstable.

原文???core.languages.en_GB???
頁(從 - 到)1501-1526
頁數26
期刊Communications on Pure and Applied Analysis
12
發行號3
DOIs
出版狀態已出版 - 5月 2013

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