Hyperbolic phase transitions in traffic flow. (English) Zbl 1037.35043

The author studies the phase transition problem within the traffic flow modelled by a \(2 \times 2\) system of hyperbolic conservation laws. The coupling is represented by a free boundary where the phase transition takes place. The global solvability of the Riemann problem is proven. Further, the author studies the global (in time) solvability of the Cauchy problem. Its global solvability is obtained without any assumption about small initial data or on the number of phase transitions.


35L65 Hyperbolic conservation laws
90B20 Traffic problems in operations research
35L45 Initial value problems for first-order hyperbolic systems
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