{
  "id": "1703.09882",
  "version": "v1",
  "published": "2017-03-29T04:24:14.000Z",
  "updated": "2017-03-29T04:24:14.000Z",
  "title": "Classification of certain qualitative properties of solutions for the quasilinear parabolic equations",
  "authors": [
    "Yan Li",
    "Zhengce Zhang",
    "Liping Zhu"
  ],
  "comment": "accepted for publication in SCIENCE CHINA Mathematics",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we mainly consider the initial boundary problem for a quasilinear parabolic equation \\[ u_t-\\mathrm{div}\\left(|\\nabla u|^{p-2}\\nabla u\\right)=-|u|^{\\beta-1}u+\\alpha|u|^{q-2}u, \\] where $p>1,\\beta>0$, $q\\geq1$ and $\\alpha>0$. By using Gagliardo-Nirenberg type inequality, energy method and comparison principle, the phenomena of blowup and extinction are classified completely in the different ranges of reaction exponents.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-29T04:24:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quasilinear parabolic equation",
      "qualitative properties",
      "classification",
      "initial boundary problem",
      "gagliardo-nirenberg type inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}