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. 其他題名： CPAA 出版日期： 2013-05-01 出處： Communications on pure and applied analysis, 2013-05, Vol.12 (3), p.1501-1526 識別號： ISSN: 1553-5258 識別號： ISSN: 1534-0392 識別號： EISSN: 1553-5258 識別號： DOI: 10.3934/cpaa.2013.12.1501
