{
  "id": "1007.4567",
  "version": "v1",
  "published": "2010-07-26T20:38:24.000Z",
  "updated": "2010-07-26T20:38:24.000Z",
  "title": "Finite-dimensional global attractors in Banach spaces",
  "authors": [
    "Alexandre N Carvalho",
    "José A Langa",
    "James C Robinson"
  ],
  "categories": [
    "math.AP",
    "math.DS"
  ],
  "abstract": "We provide bounds on the upper box-counting dimension of negatively invariant subsets of Banach spaces, a problem that is easily reduced to covering the image of the unit ball under a linear map by a collection of balls of smaller radius. As an application of the abstract theory we show that the global attractors of a very broad class of parabolic partial differential equations (semilinear equations in Banach spaces) are finite-dimensional.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-26T20:38:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "banach spaces",
      "finite-dimensional global attractors",
      "parabolic partial differential equations",
      "semilinear equations",
      "negatively invariant subsets"
    ],
    "publication": {
      "doi": "10.1016/j.jde.2010.09.032",
      "journal": "Journal of Differential Equations",
      "year": 2010,
      "volume": 249,
      "number": 12,
      "pages": 3099
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010JDE...249.3099C"
    }
  }
}