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 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.