{
  "id": "2004.08486",
  "version": "v1",
  "published": "2020-04-17T23:24:00.000Z",
  "updated": "2020-04-17T23:24:00.000Z",
  "title": "Critical exponent for semi-linear structurally damped wave equation of derivative type",
  "authors": [
    "Tuan Anh Dao",
    "Ahmad Z. Fino"
  ],
  "comment": "8 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "Main purpose of this paper is to study the following semi-linear structurally damped wave equation with nonlinearity of derivative type: $$u_{tt}- \\Delta u+ \\mu(-\\Delta)^{\\sigma/2} u_t= |u_t|^p,\\quad u(0,x)= u_0(x),\\quad u_t(0,x)=u_1(x),$$ with $\\mu>0$, $n\\geq1$, $\\sigma \\in (0,2]$ and $p>1$. In particular, we are going to prove the non-existence of global weak solutions by using a new test function and suitable sign assumptions on the initial data in both the subcritical case and the critical case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-17T23:24:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B44",
      "35L76",
      "35L71",
      "35A01"
    ],
    "keywords": [
      "semi-linear structurally damped wave equation",
      "derivative type",
      "critical exponent",
      "global weak solutions",
      "main purpose"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}