{
  "id": "0807.4657",
  "version": "v1",
  "published": "2008-07-29T13:39:00.000Z",
  "updated": "2008-07-29T13:39:00.000Z",
  "title": "Non-diffusive large time behaviour for a degenerate viscous Hamilton-Jacobi equation",
  "authors": [
    "Philippe Laurençot"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The convergence to non-diffusive self-similar solutions is investigated for non-negative solutions to the Cauchy problem $\\partial_t u = \\Delta_p u + |\\nabla u|^q$ when the initial data converge to zero at infinity. Sufficient conditions on the exponents $p>2$ and $q>1$ are given that guarantee that the diffusion becomes negligible for large times and the $L^\\infty$-norm of $u(t)$ converges to a positive value as $t\\to\\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-07-29T13:39:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35K65",
      "35K55",
      "49L25"
    ],
    "keywords": [
      "degenerate viscous hamilton-jacobi equation",
      "non-diffusive large time behaviour",
      "initial data converge",
      "self-similar solutions",
      "cauchy problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.4657L"
    }
  }
}