{
  "id": "math/0503171",
  "version": "v1",
  "published": "2005-03-09T05:50:24.000Z",
  "updated": "2005-03-09T05:50:24.000Z",
  "title": "Existence and blow up of small-amplitude nonlinear waves with a sign-changing potential",
  "authors": [
    "Paschalis Karageorgis"
  ],
  "comment": "34 pages, 1 figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the nonlinear wave equation with a sign-changing potential in any space dimension. If the potential is small and rapidly decaying, then the existence of small-amplitude solutions is driven by the nonlinear term. If the potential induces growth in the linearized problem, however, solutions that start out small may blow-up in finite time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-03-09T05:50:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35C15",
      "35L05",
      "35L15"
    ],
    "keywords": [
      "small-amplitude nonlinear waves",
      "sign-changing potential",
      "nonlinear wave equation",
      "potential induces growth",
      "finite time"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.jde.2005.02.020",
      "journal": "Journal of Differential Equations",
      "year": 2005,
      "volume": 219,
      "number": 2,
      "pages": 259
    },
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005JDE...219..259K"
    }
  }
}