The zero relaxation limit for the Aw-Rascle-Zhang traffic flow model - Archive ouverte HAL Access content directly
Journal Articles Zeitschrift für Angewandte Mathematik und Physik Year : 2019

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

(1, 2, 3) , (1, 2, 3, 4)
1
2
3
4

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.
Fichier principal
Vignette du fichier
Goatin Laurent-Brouty - 2019.pdf (348.69 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01760930 , version 1 (06-04-2018)
hal-01760930 , version 2 (07-12-2018)
hal-01760930 , version 3 (11-04-2019)

Identifiers

Cite

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

Altmetric

Share

Gmail Facebook Twitter LinkedIn More