{
  "id": "math/0404420",
  "version": "v2",
  "published": "2004-04-22T19:46:20.000Z",
  "updated": "2005-04-08T19:05:08.000Z",
  "title": "Global existence for Dirichlet-wave equations with quadratic nonlinearties in high dimensions",
  "authors": [
    "Jason Metcalfe",
    "Christopher D. Sogge"
  ],
  "comment": "Some corrections (per the referee's suggestions) were made in Section 3. 24 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove global existence of solutions to quasilinear wave equations with quadratic nonlinearities exterior to nontrapping obstacles in spatial dimensions four and higher. This generalizes a result of Shibata and Tsutsumi in spatial dimensions greater than or equal to six. The technique of proof would allow for more complicated geometries provided that an appropriate local energy decay exists for the associated linear wave equation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-04-08T19:05:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L70",
      "42B99"
    ],
    "keywords": [
      "global existence",
      "dirichlet-wave equations",
      "quadratic nonlinearties",
      "high dimensions",
      "appropriate local energy decay"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......4420M"
    }
  }
}