Localisation of perturbations of a constant state in a traffic flow model

Tej-Eddine Ghoul, Nader Masmoudi, Eliot Pacherie

Published 2022-04-25Version 1

We consider, in the Aw-Rascle-Zhang traffic flow model, the problem of the asymptotic stability of constant flows. By using a perturbative approach, we show the stability in a larger space of perturbation than previous results. Furthermore, we are able to compute where the perturbation is mainly localised in space for a given time, based on the localisation of the perturbation initially. These new ideas can be applied to various other models of hyperbolic conservation laws with relaxations.