{
  "id": "2312.12886",
  "version": "v1",
  "published": "2023-12-20T09:51:31.000Z",
  "updated": "2023-12-20T09:51:31.000Z",
  "title": "A note on nonlocal approximations of sign-unrestricted solutions of conservation laws",
  "authors": [
    "Alexander Keimer",
    "Lukas Pflug"
  ],
  "comment": "13 pages, 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the singular limit problem for nonlocal conservation laws in which the sign of the initial datum is unrestricted and the velocity of the conservation law depends on a nonlocal approximation of the absolute value of the density. We demonstrate that the nonlocal solutions converge to the local entropy solution when the nonlocal kernel tends to a Dirac distribution, and thus obtain an approximation result for local unsigned conservation laws, generalizing the current results on the so-called sign-restricted singular limit problem. The considered model class covers special cases like a generalized Burgers' equation and scalar versions of the Keyfitz--Kranzer system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-20T09:51:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L65",
      "35L04"
    ],
    "keywords": [
      "nonlocal approximation",
      "sign-unrestricted solutions",
      "singular limit problem",
      "model class covers special cases",
      "nonlocal kernel tends"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}