Journal
SIAM JOURNAL ON APPLIED MATHEMATICS
Volume 63, Issue 2, Pages 708-721Publisher
SIAM PUBLICATIONS
DOI: 10.1137/S0036139901393184
Keywords
hyperbolic conservation laws; phase transitions; macroscopic vehicular traffic model; hyperbolic systems; partial differential equations
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This paper provides a mathematical model of the phenomenon of phase transitions in traffic flow. The model consists of a scalar conservation law coupled with a 2 x 2 system of conservation laws. The coupling is achieved via a free boundary, where the phase transition takes place. For this model, the Riemann problem is stated and globally solved. The Cauchy problem is proved to admit a solution defined globally in time without any assumption about the smallness of the initial data or the number of phase boundaries. Qualitative properties of real traffic flow are shown to agree with properties of the solutions of the model.
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