{
  "id": "1902.01127",
  "version": "v1",
  "published": "2019-02-04T11:22:24.000Z",
  "updated": "2019-02-04T11:22:24.000Z",
  "title": "Continuation beyond interior gradient blow-up in a semilinear parabolic equation",
  "authors": [
    "Marek Fila",
    "Johannes Lankeit"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "It is known that there is a class of semilinear parabolic equations for which interior gradient blow-up (in finite time) occurs for some solutions. We construct a continuation of such solutions after gradient blow-up. This continuation is global in time and we give an example when it never becomes a classical solution again.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-04T11:22:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K55",
      "35B44"
    ],
    "keywords": [
      "interior gradient blow-up",
      "semilinear parabolic equation",
      "continuation",
      "finite time",
      "classical solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}