{
  "id": "1202.6072",
  "version": "v1",
  "published": "2012-02-27T21:16:35.000Z",
  "updated": "2012-02-27T21:16:35.000Z",
  "title": "The influence of fractional diffusion in Fisher-KPP equations",
  "authors": [
    "Xavier Cabre",
    "Jean-Michel Roquejoffre"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the Fisher-KPP equation where the Laplacian is replaced by the generator of a Feller semigroup with power decaying kernel, an important example being the fractional Laplacian. In contrast with the case of the stan- dard Laplacian where the stable state invades the unstable one at constant speed, we prove that with fractional diffusion, generated for instance by a stable L\\'evy process, the front position is exponential in time. Our results provide a mathe- matically rigorous justification of numerous heuristics about this model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-02-27T21:16:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K57"
    ],
    "keywords": [
      "fractional diffusion",
      "fisher-kpp equation",
      "dard laplacian",
      "stable levy process",
      "feller semigroup"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00220-013-1682-5",
      "journal": "Communications in Mathematical Physics",
      "year": 2013,
      "month": "Jun",
      "volume": 320,
      "number": 3,
      "pages": 679
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013CMaPh.320..679C"
    }
  }
}