{
  "id": "1810.03780",
  "version": "v1",
  "published": "2018-10-09T02:33:21.000Z",
  "updated": "2018-10-09T02:33:21.000Z",
  "title": "The lifespan of solutions of semilinear wave equations with the scale invariant damping in one space dimension",
  "authors": [
    "Masakazu Kato",
    "Hiroyuki Takamura",
    "Kyouhei Wakasa"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "The critical constant of time-decaying damping in the scale invari- ant case is recently conjectured. It also has been expected that the lifespan estimate is the same as associated semilinear heat equations if the constant is in \"heat-like\" domain. In this paper, we point out that this is not true if the total integral of the sum of initial position and speed vanishes. In such a case, we have a new type of the lifespan estimates which is closely related to the non-damped case in shifted space dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-09T02:33:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L71",
      "35B44"
    ],
    "keywords": [
      "semilinear wave equations",
      "scale invariant damping",
      "lifespan estimate",
      "associated semilinear heat equations",
      "shifted space dimensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}