{
  "id": "1602.03339",
  "version": "v1",
  "published": "2016-02-10T12:09:55.000Z",
  "updated": "2016-02-10T12:09:55.000Z",
  "title": "Attractors for the strongly damped wave equation with $p$-Laplacian",
  "authors": [
    "Azer Khanmamedov",
    "Zehra Şen"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper is concerned with the initial boundary value problem for one dimensional strongly damped wave equation involving $p$-Laplacian. For $p>2$, we establish the existence of weak local attractors for this problem in $W_{0}^{1,p}(0,1)\\times L^{2}(0,1)$. Under restriction $2<p<4$, we prove that the semigroup, generated by the considered problem, possesses a strong global attractor in $W_{0}^{1,p}(0,1)\\times L^{2}(0,1)$ and this attractor is a bounded subset of $W^{1,\\infty }(0,1)\\times W^{1,\\infty }(0,1)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-10T12:09:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L05",
      "35L30",
      "35B41"
    ],
    "keywords": [
      "initial boundary value problem",
      "dimensional strongly damped wave equation",
      "weak local attractors",
      "strong global attractor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160203339K"
    }
  }
}