{
  "id": "1309.6173",
  "version": "v1",
  "published": "2013-09-24T14:18:27.000Z",
  "updated": "2013-09-24T14:18:27.000Z",
  "title": "Rate of Convergence to Barenblatt Profiles for the Fast Diffusion Equation with a Critical Exponent",
  "authors": [
    "Marek Fila",
    "John R. King",
    "Michael Winkler"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the asymptotic behaviour near extinction of positive solutions of the Cauchy problem for the fast diffusion equation with a critical exponent. After a suitable rescaling which yields a non--linear Fokker--Planck equation, we find a continuum of algebraic rates of convergence to a self--similar profile. These rates depend explicitly on the spatial decay rates of initial data. This improves a previous result on slow convergence for the critical fast diffusion equation ({\\sc Bonforte et al}. in Arch Rat Mech Anal 196:631--680, 2010) and provides answers to some open problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-24T14:18:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical exponent",
      "barenblatt profiles",
      "arch rat mech anal",
      "critical fast diffusion equation",
      "non-linear fokker-planck equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.6173F"
    }
  }
}