{
  "id": "1404.6195",
  "version": "v3",
  "published": "2014-04-24T17:41:51.000Z",
  "updated": "2014-07-24T11:03:14.000Z",
  "title": "Existence, Uniqueness and Asymptotic behaviour for fractional porous medium equations on bounded domains",
  "authors": [
    "Matteo Bonforte",
    "Yannick Sire",
    "Juan Luis Vazquez"
  ],
  "comment": "Keywords: Fractional Laplace operators, Porous Medium diffusion, Existence and uniqueness theory, Asymptotic behaviour, Fractional Sobolev Spaces",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider nonlinear diffusive evolution equations posed on bounded space domains, governed by fractional Laplace-type operators, and involving porous medium type nonlinearities. We establish existence and uniqueness results in a suitable class of solutions using the theory of maximal monotone operators on dual spaces. Then we describe the long-time asymptotics in terms of separate-variables solutions of the friendly giant type. As a by-product, we obtain an existence and uniqueness result for semilinear elliptic non local equations with sub-linear nonlinearities. The Appendix contains a review of the theory of fractional Sobolev spaces and of the interpolation theory that are used in the rest of the paper.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-07-24T11:03:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "35K61",
      "35K65",
      "35B40",
      "35A01",
      "35A02"
    ],
    "keywords": [
      "fractional porous medium equations",
      "asymptotic behaviour",
      "bounded domains",
      "diffusive evolution equations",
      "semilinear elliptic non local equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.6195B"
    }
  }
}