{
  "id": "2112.01733",
  "version": "v2",
  "published": "2021-12-03T06:13:12.000Z",
  "updated": "2022-03-30T15:12:29.000Z",
  "title": "The generalized porous medium equation on graphs: existence and uniqueness of solutions with $\\ell^1$ data",
  "authors": [
    "Davide Bianchi",
    "Alberto G. Setti",
    "Radoslaw K. Wojciechowski"
  ],
  "categories": [
    "math.AP",
    "math.CO"
  ],
  "abstract": "We study solutions of the generalized porous medium equation on infinite graphs. For nonnegative or nonpositive integrable data, we prove the existence and uniqueness of mild solutions on any graph. For changing sign integrable data, we show existence and uniqueness under extra assumptions such as local finiteness or a uniform lower bound on the node measure.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-03-30T15:12:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "35A01",
      "35A02",
      "76S05",
      "05C22",
      "05C63",
      "47H06"
    ],
    "keywords": [
      "generalized porous medium equation",
      "uniqueness",
      "uniform lower bound",
      "infinite graphs",
      "mild solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}