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

  • Paola Goatin
  • Nicolas Laurent-BroutyEmail author
Article
  • 11 Downloads

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 wavefront 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.

Keywords

Hyperbolic systems of conservation laws with relaxation Temple class systems Decay estimates Wavefront tracking Macroscopic traffic flow models 

Mathematics Subject Classification

35L65 35L45 90B20 

Notes

Acknowledgements

The authors thank Debora Amadori and Graziano Guerra for insightful discussions.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Inria Sophia Antipolis - MéditerranéeUniversité Côte d’Azur, Inria, CNRS, LJADSophia AntipolisFrance
  2. 2.Ecole des Ponts ParisTechChamps-sur-MarneFrance

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