{
  "id": "2007.07655",
  "version": "v1",
  "published": "2020-07-15T12:30:26.000Z",
  "updated": "2020-07-15T12:30:26.000Z",
  "title": "A Triviality Result for Semilinear Parabolic Equations",
  "authors": [
    "Giovanni Catino",
    "Daniele Castorina",
    "Carlo Mantegazza"
  ],
  "categories": [
    "math.AP",
    "math.DG"
  ],
  "abstract": "We show a triviality result for \"pointwise\" monotone in time, bounded \"eternal\" solutions of the semilinear heat equation \\begin{equation*} u_{t}=\\Delta u + |u|^{p} \\end{equation*} on complete Riemannian manifolds of dimension $n \\geq 5$ with nonnegative Ricci tensor, when $p$ is smaller than the critical Sobolev exponent $\\frac{n+2}{n-2}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-15T12:30:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "semilinear parabolic equations",
      "triviality result",
      "semilinear heat equation",
      "complete riemannian manifolds",
      "nonnegative ricci tensor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}