{
  "id": "0910.3588",
  "version": "v1",
  "published": "2009-10-19T15:20:14.000Z",
  "updated": "2009-10-19T15:20:14.000Z",
  "title": "Attractors for nonlinear reaction-diffusion systems in unbounded domains via the method of short trajectories",
  "authors": [
    "Maurizio Grasselli",
    "Dalibor Pražák",
    "Giulio Schimperna"
  ],
  "categories": [
    "math.AP",
    "math.DS"
  ],
  "abstract": "We consider a nonlinear reaction-diffusion equation settled on the whole euclidean space. We prove the well-posedness of the corresponding Cauchy problem in a general functional setting, namely, when the initial datum is uniformly locally bounded in L^2. Then we adapt the short trajectory method to establish the existence of the global attractor and, if the space dimension is at most 3, we also find an upper bound of its Kolmogorov's entropy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-19T15:20:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B41",
      "35K57",
      "92D25"
    ],
    "keywords": [
      "nonlinear reaction-diffusion systems",
      "unbounded domains",
      "short trajectory method",
      "cauchy problem",
      "kolmogorovs entropy"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1016/j.jde.2010.06.001",
      "journal": "Journal of Differential Equations",
      "year": 2010,
      "volume": 249,
      "number": 9,
      "pages": 2287
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010JDE...249.2287G"
    }
  }
}