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

Paola Goatin (1, 2, 3) , Nicolas Laurent-Brouty (1, 2, 3)

1 ACUMES - Analysis and Control of Unsteady Models for Engineering Sciences
2 LJAD - Laboratoire Jean Alexandre Dieudonné
3 COMUE UCA - COMUE Université Côte d'Azur (2015-2019)

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.

Mots clés: Hyperbolic systems of conservation laws with relaxation; Temple class systems; macroscopic traffic flow models; wave-front tracking; decay estimates

Domaines: Equations aux dérivées partielles [math.AP]

Paola Goatin, Nicolas Laurent-Brouty. The zero relaxation limit for the Aw-Rascle-Zhang traffic flow model. Zeitschrift für Angewandte Mathematik und Physik, inPress. ⟨hal-01760930v2⟩