{
  "id": "1912.06490",
  "version": "v1",
  "published": "2019-12-12T15:50:18.000Z",
  "updated": "2019-12-12T15:50:18.000Z",
  "title": "Global existence and decay estimates for the heat equation with exponential nonlinearity",
  "authors": [
    "Mohamed Majdoub",
    "Slim Tayachi"
  ],
  "comment": "To appear. arXiv admin note: text overlap with arXiv:1607.02723, arXiv:1606.07320",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "In this paper we consider the initial value {problem $\\partial_{t} u- \\Delta u=f(u),$ $u(0)=u_0\\in exp\\,L^p(\\mathbb{R}^N),$} where $p>1$ and $f : \\mathbb{R}\\to\\mathbb{R}$ having an exponential growth at infinity with $f(0)=0.$ Under smallness condition on the initial data and for nonlinearity $f$ {such that $|f(u)|\\sim \\mbox{e}^{|u|^q}$ as $|u|\\to \\infty$,} $|f(u)|\\sim |u|^{m}$ as $u\\to 0,$ $0<q\\leq p\\leq\\,m,\\;{N(m-1)\\over 2}\\geq p>1$, we show that the solution is global. Moreover, we obtain decay estimates in Lebesgue spaces for large time which depend on $m.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-12T15:50:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "decay estimates",
      "exponential nonlinearity",
      "global existence",
      "heat equation",
      "initial value"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}