{
  "id": "1606.07320",
  "version": "v1",
  "published": "2016-06-23T14:23:38.000Z",
  "updated": "2016-06-23T14:23:38.000Z",
  "title": "Local well-posedness and global existence for the biharmonic heat equation with exponential nonlinearity",
  "authors": [
    "Mohamed Majdoub",
    "Sarah Otsmane",
    "Slim Tayachi"
  ],
  "comment": "Submitted",
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "In this paper we prove local well-posedness in Orlicz spaces for the biharmonic heat equation $\\partial_{t} u+ \\Delta^2 u=f(u),\\;t>0,\\;x\\in\\R^N,$ with $f(u)\\sim \\mbox{e}^{u^2}$ for large $u.$ Under smallness condition on the initial data and for exponential nonlinearity $f$ such that $f(u)\\sim u^m$ as $u\\to 0,$ $m$ integer and $N(m-1)/4\\geq 2$, we show that the solution is global. Moreover, we obtain a decay estimates for large time for the nonlinear biharmonic heat equation as well as for the nonlinear heat equation. Our results extend to the nonlinear polyharmonic heat equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-23T14:23:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local well-posedness",
      "exponential nonlinearity",
      "global existence",
      "nonlinear polyharmonic heat equation",
      "nonlinear biharmonic heat equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}