{
  "id": "1308.1361",
  "version": "v2",
  "published": "2013-08-06T18:00:23.000Z",
  "updated": "2013-12-15T20:29:32.000Z",
  "title": "Classification of positive solutions of heat equation with supercritical absorption",
  "authors": [
    "Konstantinos Gkikas",
    "Laurent Veron"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $q\\geq 1+\\frac{2}{N}$. We prove that any positive solution of (E) $\\prt_t u-\\xD u+u^q=0$ in $\\mathbb{R}^N\\times(0,\\infty)$ admits an initial trace which is a nonnegative Borel measure, outer regular with respect to the fine topology associated to the Bessel capacity $C_{\\frac{2}{q},q'}$ in $\\BBR^N$ ($q'=q/q-1)$) and absolutely continuous with respect to this capacity. If $\\nu$ is a nonnegative Borel measure in $\\BBR^N$ with the above properties we construct a positive solution $u$ of (E) with initial trace $\\gn$ and we prove that this solution is the unique $\\gs$-moderate solution of (E) with such an initial trace. Finally we prove that every positive solution of (E) is $\\gs$-moderate.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-15T20:29:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive solution",
      "heat equation",
      "supercritical absorption",
      "initial trace",
      "nonnegative borel measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.1361G"
    }
  }
}