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An existence result for a constrained two-phase transition model with metastable phase for vehicular traffic. (English) Zbl 1415.35260

The authors investigate a constrained phase transition model of hyperbolic conservation laws with application in the vehicular light or heavy traffic flows. They consider the Lighthill-Whitham-Richards model in the free-flow phase and the Aw-Rascle-Zhang model in the congested phase. By applying the wave-front tracking method, the authors prove the global existence of solutions for constrained Cauchy problems.

MSC:

35Q90 PDEs in connection with mathematical programming
35L65 Hyperbolic conservation laws
90B20 Traffic problems in operations research
35L45 Initial value problems for first-order hyperbolic systems
35A01 Existence problems for PDEs: global existence, local existence, non-existence
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References:

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