{
  "id": "1001.0410",
  "version": "v2",
  "published": "2010-01-03T21:08:28.000Z",
  "updated": "2010-02-01T16:16:23.000Z",
  "title": "Nonlinear porous medium flow with fractional potential pressure",
  "authors": [
    "Luis A. Caffarelli",
    "Juan L. Vazquez"
  ],
  "comment": "32 pages, Latex",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study a porous medium equation, with nonlocal diffusion effects given by an inverse fractional Laplacian operator. We pose the problem in n-dimensional space for all t>0 with bounded and compactly supported initial data, and prove existence of a weak and bounded solution that propagates with finite speed, a property that is nor shared by other fractional diffusion models.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-02-01T16:16:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "35K65"
    ],
    "keywords": [
      "nonlinear porous medium flow",
      "fractional potential pressure",
      "inverse fractional laplacian operator",
      "nonlocal diffusion effects",
      "fractional diffusion models"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00205-011-0420-4",
      "journal": "Archive for Rational Mechanics and Analysis",
      "year": 2011,
      "month": "Nov",
      "volume": 202,
      "number": 2,
      "pages": 537
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011ArRMA.202..537C"
    }
  }
}