{
  "id": "1001.2383",
  "version": "v1",
  "published": "2010-01-14T08:24:42.000Z",
  "updated": "2010-01-14T08:24:42.000Z",
  "title": "A fractional porous medium equation",
  "authors": [
    "Arturo de Pablo",
    "Fernando Quiros",
    "Ana Rodriguez",
    "Juan Luis Vazquez"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We develop a theory of existence, uniqueness and regularity for a porous medium equation with fractional diffusion, $\\frac{\\partial u}{\\partial t} + (-\\Delta)^{1/2} (|u|^{m-1}u)=0$ in $\\mathbb{R}^N$, with $m>m_*=(N-1)/N$, $N\\ge1$ and $f\\in L^1(\\mathbb{R}^N)$. An $L^1$-contraction semigroup is constructed and the continuous dependence on data and exponent is established. Nonnegative solutions are proved to be continuous and strictly positive for all $x\\in\\mathbb{R}^N$, $t>0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-01-14T08:24:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A33",
      "35K55"
    ],
    "keywords": [
      "fractional porous medium equation",
      "fractional diffusion",
      "contraction semigroup",
      "regularity",
      "continuous dependence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1001.2383D"
    }
  }
}