{
  "id": "2404.10368",
  "version": "v1",
  "published": "2024-04-16T08:04:32.000Z",
  "updated": "2024-04-16T08:04:32.000Z",
  "title": "Non-local traffic flow models with time delay: well-posedness and numerical approximation",
  "authors": [
    "Ilaria Ciaramaglia",
    "Paola Goatin",
    "Gabriella Puppo"
  ],
  "categories": [
    "math.AP",
    "cs.NA",
    "math.NA"
  ],
  "abstract": "We prove the well-posedness of weak entropy solutions of a scalar non-local traffic flow model with time delay. Existence is obtained by convergence of finite volume approximate solutions constructed by Lax-Friedrich and Hilliges-Weidlich schemes, while the L1 stability with respect to the initial data and the delay parameter relies on a Kruzkov-type doubling of variable technique.Numerical tests are provided to illustrate the efficiency of the proposed schemes, as well as the solution dependence on the delay and look-ahead parameters.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-16T08:04:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "time delay",
      "numerical approximation",
      "scalar non-local traffic flow model",
      "well-posedness",
      "finite volume approximate solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}