{
  "id": "math/0701774",
  "version": "v1",
  "published": "2007-01-26T15:41:06.000Z",
  "updated": "2007-01-26T15:41:06.000Z",
  "title": "A Gamma-convergence argument for the blow-up of a non-local semilinear parabolic equation with Neumann boundary conditions",
  "authors": [
    "Ahmad El Soufi",
    "Mustapha Jazar",
    "Régis Monneau"
  ],
  "journal": "Annales de l'Institut Henri Poincar\\'{e} Analyse non lin\\'{e}aire 24 (2007) 17--39",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we study a simple non-local semilinear parabolic equation with Neumann boundary condition. We give local existence result and prove global existence for small initial data. A natural non increasing in time energy is associated to this equation. We prove that the solution blows up at finite time $T$ if and only if its energy is negative at some time before $T$. The proof of this result is based on a Gamma-convergence technique.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-01-26T15:41:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B35",
      "35B40",
      "35K55"
    ],
    "keywords": [
      "neumann boundary condition",
      "gamma-convergence argument",
      "simple non-local semilinear parabolic equation",
      "local existence result"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1774E"
    }
  }
}