{
  "id": "math/0609750",
  "version": "v1",
  "published": "2006-09-27T11:28:08.000Z",
  "updated": "2006-09-27T11:28:08.000Z",
  "title": "Asymptotic behavior for a viscous Hamilton-Jacobi equation with critical exponent",
  "authors": [
    "Thierry Gallay",
    "Philippe Laurençot"
  ],
  "comment": "17 pages, no figure",
  "categories": [
    "math.AP"
  ],
  "abstract": "The large time behavior of non-negative solutions to the viscous Hamilton-Jacobi equation $u_t - \\Delta u + |\\nabla u|^q = 0$ in the whole space $R^N$ is investigated for the critical exponent $q = (N+2)/(N+1)$. Convergence towards a rescaled self-similar solution of the linear heat equation is shown, the rescaling factor being $(\\log(t))^{-(N+1)}$. The proof relies on the construction of a one-dimensional invariant manifold for a suitable truncation of the equation written in self-similar variables.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-09-27T11:28:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B33",
      "35B40",
      "35K55",
      "37L25"
    ],
    "keywords": [
      "viscous hamilton-jacobi equation",
      "critical exponent",
      "asymptotic behavior",
      "large time behavior",
      "one-dimensional invariant manifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9750G"
    }
  }
}