{
  "id": "1407.6750",
  "version": "v2",
  "published": "2014-07-24T22:35:20.000Z",
  "updated": "2015-07-21T01:50:51.000Z",
  "title": "Combined effects of two nonlinearities in lifespan of small solutions to semi-linear wave equations",
  "authors": [
    "Kunio Hidano",
    "Chengbo Wang",
    "Kazuyoshi Yokoyama"
  ],
  "comment": "Substantially revised and expanded. 22 pages, 5 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper investigates the combined effects of two distinctive power-type nonlinear terms (with parameters $p,q>1$) in the lifespan of small solutions to semi-linear wave equations. We determine the full region of $(p,q)$ to admit global existence of small solutions, at least for spatial dimensions $n=2, 3$. Moreover, for many $(p,q)$ when there is no global existence, we obtain sharp lower bound of the lifespan, which is of the same order as the upper bound of the lifespan.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-24T22:35:20.000Z",
      "abstract": "This paper investigates combined effects of two nonlinearities in lifespan of small solutions to semi-linear wave equations. Using the method of vector fields in Klainerman (Comm. Pure Appl. Math. 38 (1985), 321--332) together with some of techniques developed in Li and Zhou (Indiana Univ. Math. J. 44 (1995), 1207--1248), we show that the upper bound on the lifespan recently obtained by Han and Zhou (Comm. Partial Differential Equations 39 (2014), 651--665) is sharp in general, at least in space dimensions n=2, 3. Moreover, we also show that in the threshold case, the equation admits global (in time) solutions.",
      "comment": "29 pages, no figures",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-07-21T01:50:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L05",
      "35L15",
      "35L71"
    ],
    "keywords": [
      "semi-linear wave equations",
      "small solutions",
      "nonlinearities",
      "equation admits global",
      "partial differential equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.6750H"
    }
  }
}