{
  "id": "1312.1652",
  "version": "v1",
  "published": "2013-12-05T19:41:33.000Z",
  "updated": "2013-12-05T19:41:33.000Z",
  "title": "Fractional Fokker-Planck equation",
  "authors": [
    "Isabelle Tristani"
  ],
  "comment": "17 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper deals with the long time behavior of solutions to a \"fractional Fokker-Planck\" equation of the form $\\partial_t f = I[f] + \\text{div}(xf)$ where the operator $I$ stands for a fractional Laplacian. We prove an exponential in time convergence towards equilibrium in new spaces. Indeed, such a result was already obtained in a $L^2$ space with a weight prescribed by the equilibrium in \\cite{GI}. We improve this result obtaining the convergence in a $L^1$ space with a polynomial weight. To do that, we take advantage of the recent paper \\cite{GMM} in which an abstract theory of enlargement of the functional space of the semigroup decay is developed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-05T19:41:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractional fokker-planck equation",
      "long time behavior",
      "semigroup decay",
      "paper deals",
      "time convergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.1652T"
    }
  }
}