{
  "id": "2406.00950",
  "version": "v1",
  "published": "2024-06-03T03:06:32.000Z",
  "updated": "2024-06-03T03:06:32.000Z",
  "title": "A Sufficient Condition for Blowup of the Nonlinear Klein-Gordon Equation with Positive Initial Energy in FLRW Spacetimes",
  "authors": [
    "Jonathon McCollum",
    "Gregory Mwamba",
    "Jesús Oliver"
  ],
  "comment": "15 pages. 1 figure",
  "journal": "Nonlinear Analysis, Volume 246, 2024, 113582, ISSN 0362-546",
  "doi": "10.1016/j.na.2024.113582",
  "categories": [
    "math.AP",
    "gr-qc"
  ],
  "abstract": "In this paper we demonstrate a sufficient condition for blowup of the nonlinear Klein-Gordon equation with arbitrarily positive initial energy in Friedmann-Lema\\^itre-Robertson-Walker spacetimes. This is accomplished using an established concavity method that has been employed for similar PDEs in Minkowski space. This proof relies on the energy inequality associated with this equation, $E(t_0)\\geq E(t)$, also proved herein using a geometric method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-03T03:06:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear klein-gordon equation",
      "sufficient condition",
      "flrw spacetimes",
      "energy inequality",
      "geometric method"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}