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



14/02/2019 - 11:00 Mr Nicolas Laurent-Brouty (Inria Sophia Antipolis) Salle 106 - Batiment IMAG

In this talk we will detail the mathematical behavior of the Aw-Rascle-Zhang model with relaxation. This model, which consists in a 2x2 hyperbolic system of  balance laws, can now be considered as a classical traffic flow model. 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 admits a limit. We then show that the limit is 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.