Journal article
Global solutions and zero relaxation limit for a traffic flow model
SIAM journal on applied mathematics, Vol.61(3), pp.1042-1061
10/25/2000
DOI: 10.1137/S0036139999356788
Abstract
We construct global solutions and study their relaxation limit for a system of nonlinear hyperbolic conservation laws with relaxation arising in traffic flows.
The system of nonlinear hyperbolic conservation laws with relaxation was derived as a nonequilibrium continuum model of traffic flows. The purpose of the new model is to address the anisotropic feature of traffic flows. The resulting hyperbolic system with relaxation is marginally stable. Thus there is no diffusion in the process of relaxation. Our analysis is vastly different from existing theory for hyperbolic conservation laws with relaxation which relies on the dissipative nature of the relaxation process. Our analysis is based on a generalized Glimm scheme. For initial data with bounded total variation, we prove that the total variation of the solutions is bounded for all time and the bound is independent of the relaxation parameter. Thus we obtain the zero relaxation limit.
Finally, we make a comparison between our results and data measured on the I-880 freeway in California ( see [Skabardonis et al., Transportation Research Record, 1554 (1996), pp. 204-212]). The comparison shows qualitative agreement between the analytic results and the data.
Details
- Title: Subtitle
- Global solutions and zero relaxation limit for a traffic flow model
- Creators
- T Li
- Resource Type
- Journal article
- Publication Details
- SIAM journal on applied mathematics, Vol.61(3), pp.1042-1061
- Publisher
- SIAM PUBLICATIONS
- DOI
- 10.1137/S0036139999356788
- ISSN
- 0036-1399
- eISSN
- 1095-712X
- Number of pages
- 20
- Language
- English
- Date published
- 10/25/2000
- Academic Unit
- Mathematics
- Record Identifier
- 9984241156902771
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