Journal article
Stability of a traffic flow model with nonconvex relaxation
Communications in mathematical sciences, Vol.3(2), pp.101-118
06/01/2005
DOI: 10.4310/CMS.2005.v3.n2.a1
Abstract
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 tra ffi c 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.
Details
- Title: Subtitle
- Stability of a traffic flow model with nonconvex relaxation
- Creators
- Tong Li - University of Iowa, MathematicsHailiang Liu - Iowa State University
- Resource Type
- Journal article
- Publication Details
- Communications in mathematical sciences, Vol.3(2), pp.101-118
- DOI
- 10.4310/CMS.2005.v3.n2.a1
- ISSN
- 1539-6746
- eISSN
- 1945-0796
- Publisher
- INT PRESS BOSTON, INC
- Number of pages
- 18
- Language
- English
- Date published
- 06/01/2005
- Academic Unit
- Mathematics
- Record Identifier
- 9984242420502771
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