{
  "id": "math/0702560",
  "version": "v2",
  "published": "2007-02-19T19:11:38.000Z",
  "updated": "2007-02-20T15:26:16.000Z",
  "title": "Instability of an equilibrium with negative definite linearization",
  "authors": [
    "Michael Robinson"
  ],
  "comment": "v1: 6 pages; v2: 7 pages, fixes a glitch in the main theorem",
  "categories": [
    "math.AP",
    "math.DS"
  ],
  "abstract": "A nonlinear parabolic differential equation is presented which has at least one equilibrium. This equilibrium is shown to have a negative definite linearization, but a spectrum which includes zero. An elementary construction shows that the equilibrium is not stable.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-02-20T15:26:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37L15",
      "35Q55"
    ],
    "keywords": [
      "negative definite linearization",
      "equilibrium",
      "nonlinear parabolic differential equation",
      "instability",
      "elementary construction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......2560R"
    }
  }
}