{
  "id": "0704.3989",
  "version": "v2",
  "published": "2007-04-30T18:21:26.000Z",
  "updated": "2007-09-09T23:10:03.000Z",
  "title": "Instability of an equilibrium of a partial differential equation",
  "authors": [
    "Michael Robinson"
  ],
  "comment": "12 pages",
  "categories": [
    "math.AP",
    "math.DS"
  ],
  "abstract": "A nonlinear parabolic differential equation with a quadratic nonlinearity is presented which has at least one equilibrium. The linearization about this equilibrium is asymptotically stable, but by using a technique inspired by H. Fujita, we show that the equilibrium is unstable in the nonlinear setting. The perturbations used have the property that they are small in every $L^p$ norm, yet they result in solutions which fail to be global.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-09-09T23:10:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37L15",
      "35Q55"
    ],
    "keywords": [
      "partial differential equation",
      "equilibrium",
      "instability",
      "nonlinear parabolic differential equation",
      "quadratic nonlinearity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0704.3989R"
    }
  }
}