{
  "id": "0807.1539",
  "version": "v2",
  "published": "2008-07-09T20:32:13.000Z",
  "updated": "2008-11-11T21:24:42.000Z",
  "title": "On convergence of solutions to equilibria for quasilinear parabolic problems",
  "authors": [
    "Jan Pruess",
    "Gieri Simonett",
    "Rico Zacher"
  ],
  "comment": "33 pages. To appear in Journal of Differential Equations. Contains a more general result in Theorem 6.1 than the first version",
  "doi": "10.1016/j.jde.2008.10.034",
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "We show convergence of solutions to equilibria for quasilinear parabolic evolution equations in situations where the set of equilibria is non-discrete, but forms a finite-dimensional $C^1$-manifold which is normally hyperbolic. Our results do not depend on the presence of an appropriate Lyapunov functional as in the \\L ojasiewicz-Simon approach, but are of local nature.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-11-11T21:24:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "34G20",
      "35K55",
      "35B35",
      "37D10",
      "35R35"
    ],
    "keywords": [
      "quasilinear parabolic problems",
      "equilibria",
      "convergence",
      "quasilinear parabolic evolution equations",
      "appropriate lyapunov functional"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Differential Equations",
      "year": 2009,
      "volume": 246,
      "number": 10,
      "pages": 3902
    },
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009JDE...246.3902P"
    }
  }
}