{
  "id": "0912.3553",
  "version": "v2",
  "published": "2009-12-17T23:04:54.000Z",
  "updated": "2010-06-02T22:13:41.000Z",
  "title": "Asymptotic Behavior for a Nonlocal Diffusion Equation with Absorption and Nonintegrable Initial Data. the Supercritical Case",
  "authors": [
    "Joana Terra",
    "Noemi Wolanski"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we study the asymptotic behavior as time goes to infinity of the solution to a nonlocal diffusion equation with absorption modeled by a powerlike reaction $-u^p$, $p>1$ and set in $\\R^N$. We consider a bounded, nonnegative initial datum $u_0$ that behaves like a negative power at infinity. That is, $|x|^\\alpha u_0(x)\\to A>0$ as $|x|\\to\\infty$ with $0<\\alpha\\le N$. We prove that, in the supercritical case $p>1+2/\\alpha$, the solution behaves asymptotically as that of the heat equation --with diffusivity $\\a$ related to the nonlocal operator-- with the same initial datum.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-06-02T22:13:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K57"
    ],
    "keywords": [
      "nonlocal diffusion equation",
      "nonintegrable initial data",
      "asymptotic behavior",
      "supercritical case",
      "absorption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.3553T"
    }
  }
}