{
  "id": "2204.11557",
  "version": "v1",
  "published": "2022-04-25T11:06:10.000Z",
  "updated": "2022-04-25T11:06:10.000Z",
  "title": "Localisation of perturbations of a constant state in a traffic flow model",
  "authors": [
    "Tej-Eddine Ghoul",
    "Nader Masmoudi",
    "Eliot Pacherie"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-25T11:06:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "constant state",
      "perturbation",
      "localisation",
      "aw-rascle-zhang traffic flow model",
      "hyperbolic conservation laws"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}