Journal article
Global solutions of nonconcave hyperbolic conservation laws with relaxation arising from traffic flow
Journal of Differential Equations, Vol.190(1), pp.131-149
2003
DOI: 10.1016/S0022-0396(03)00014-7
Abstract
We establish global solutions of nonconcave hyperbolic equations with relaxation arising from traffic flow. One of the characteristic fields of the system is neither linearly degenerate nor genuinely nonlinear. Furthermore, there is no dissipative mechanism in the relaxation system. Characteristics travel no faster than traffic. The global existence and uniqueness of the solution to the Cauchy problem are established by means of a finite difference approximation. To deal with the nonconcavity, we use a modified argument of Oleinik (Amer. Math. Soc. Translations 26 (1963) 95). It is also shown that the zero relaxation limit of the solutions exists and is the unique entropy solution of the equilibrium equation.
Details
- Title: Subtitle
- Global solutions of nonconcave hyperbolic conservation laws with relaxation arising from traffic flow
- Creators
- Tong Li - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Journal of Differential Equations, Vol.190(1), pp.131-149
- DOI
- 10.1016/S0022-0396(03)00014-7
- ISSN
- 0022-0396
- eISSN
- 1090-2732
- Publisher
- Elsevier Inc
- Language
- English
- Date published
- 2003
- Academic Unit
- Mathematics
- Record Identifier
- 9984241058102771
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