{
  "id": "0709.2705",
  "version": "v1",
  "published": "2007-09-17T19:39:15.000Z",
  "updated": "2007-09-17T19:39:15.000Z",
  "title": "Classification of connecting solutions of semilinear parabolic equations",
  "authors": [
    "Michael Robinson"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "For a given semilinear parabolic equation with polynomial nonlinearity, many solutions blow up in finite time. For a certain large class of these equations, we show that some of the solutions which do not blow up actually tend to equilibria. The characterizing property of such solutions is a finite energy constraint, which comes about from the fact that this class of equations can be written as the $L^2$ gradient of a certain functional.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-09-17T19:39:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35K55"
    ],
    "keywords": [
      "semilinear parabolic equation",
      "connecting solutions",
      "classification",
      "finite energy constraint",
      "finite time"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.2705R"
    }
  }
}