# The zero relaxation limit for the Aw-Rascle-Zhang traffic flow model

Abstract : We study the behavior of the Aw-Rascle-Zhang model when the relaxation parameter converges to zero. In a Lagrangian setting, we use the Wave-Front-Tracking method with splitting technique to construct a sequence of approximate solutions. We prove that this sequence converges to a weak entropy solution of the relaxed system associated to a given initial datum with bounded variation. Besides, we also provide an estimate on the decay of positive waves. We finally prove that the solutions of the Aw-Rascle-Zhang system with relaxation converge to a weak solution of the corresponding scalar conservation law when the relaxation parameter goes to zero.
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Journal articles

Cited literature [45 references]

https://hal.inria.fr/hal-01760930
Contributor : Nicolas Laurent-Brouty <>
Submitted on : Thursday, April 11, 2019 - 11:09:53 AM
Last modification on : Friday, January 15, 2021 - 5:28:37 PM

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### Citation

Paola Goatin, Nicolas Laurent-Brouty. The zero relaxation limit for the Aw-Rascle-Zhang traffic flow model. Zeitschrift für Angewandte Mathematik und Physik, Springer Verlag, 2019, 70 (31), ⟨10.1007/s00033-018-1071-1⟩. ⟨hal-01760930v3⟩

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