{
  "id": "1411.7743",
  "version": "v1",
  "published": "2014-11-28T03:46:12.000Z",
  "updated": "2014-11-28T03:46:12.000Z",
  "title": "Existences and upper semi-continuity of pullback attractors in $H^1(\\mathbb{R}^N)$ for non-autonomous reaction-diffusion equations perturbed by multiplicative noise",
  "authors": [
    "Wenqiang Zhao"
  ],
  "comment": "29pages",
  "categories": [
    "math.AP",
    "math.DS"
  ],
  "abstract": "The existences and upper semi-continuity of $\\mathcal{D}$-pullback attractors in $H^1(\\mathbb{R}^N)$ are proved for stochastic reaction-diffusion equation on $\\mathbb{R}^N$ driven by a multiplicative noise and a deterministic non-autonomous forcing. It is also showed that the upper semi-continuity of the obtained attractors may happen in $H^1(\\mathbb{R}^N)$ at any $\\varepsilon_0\\neq0$. To solve this problem, some abstract results are given, which imply that a family of attractors obtained in \\emph{a initial space} are compact, attracting and upper semi-continuous in\\emph{ a associated non-initial space} only if some compactness conditions of the cocycles in this space are assumed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-28T03:46:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "35R60",
      "35B40",
      "35B41"
    ],
    "keywords": [
      "non-autonomous reaction-diffusion equations",
      "upper semi-continuity",
      "pullback attractors",
      "multiplicative noise",
      "existences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.7743Z"
    }
  }
}