{
  "id": "0805.2314",
  "version": "v1",
  "published": "2008-05-15T14:05:19.000Z",
  "updated": "2008-05-15T14:05:19.000Z",
  "title": "Long-time extinction of solutions of some semilinear parabolic equations",
  "authors": [
    "Yves Belaud",
    "Andrey Shishkov"
  ],
  "journal": "Journal of Differential Equations (2007) 238, pages 64-86",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the long time behaviour of solutions of semi-linear parabolic equation of the following type $\\partial_t u-\\Delta u+a_0(x)u^q=0$ where $a_0(x) \\geq d_0 \\exp(\\frac{\\omega(|x|)}{|x|^2})$, $d_0>0$, $1>q>0$ and $\\omega$ a positive continuous radial function. We give a Dini-like condition on the function $\\omega$ by two different method which implies that any solution of the above equation vanishes in a finite time. The first one is a variant of a local energy method and the second one is derived from semi-classical limits of some Schr\\\"odinger operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-05-15T14:05:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35K20",
      "35P15"
    ],
    "keywords": [
      "semilinear parabolic equations",
      "long-time extinction",
      "semi-linear parabolic equation",
      "long time behaviour",
      "local energy method"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.2314B"
    }
  }
}