Open Access
June 2005 Stability of a Traffic Flow Model with Nonconvex Relaxation
Tong Li, Hailiang Liu
Commun. Math. Sci. 3(2): 101-118 (June 2005).


This paper is concerned with the nonlinear stability of traveling wave solutions for a quasi-linear relaxation model with a nonconvex equilibrium flux. The study is motivated by and the results are applied to the well-known dynamic continuum traffic flow model, the Payne and Whitham (PW) model with a nonconcave fundamental diagram. The PW model is the first of its kind and it has been widely adopted by traffic engineers in the study of stability and instability phenomena of traffic flow. The traveling wave solutions are shown to be asymptotically stable under small disturbances and under the sub-characteristic condition using a weighted energy method. The analysis applies to both non-degenerate case and the degenerate case where the traveling wave has exponential decay rates at infinity and has an algebraic decay rate at infinity, respectively.


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Tong Li. Hailiang Liu. "Stability of a Traffic Flow Model with Nonconvex Relaxation." Commun. Math. Sci. 3 (2) 101 - 118, June 2005.


Published: June 2005
First available in Project Euclid: 14 June 2005

zbMATH: 1099.35156
MathSciNet: MR2164192

Rights: Copyright © 2005 International Press of Boston

Vol.3 • No. 2 • June 2005
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