{
  "id": "2308.06208",
  "version": "v1",
  "published": "2023-08-11T16:14:20.000Z",
  "updated": "2023-08-11T16:14:20.000Z",
  "title": "Well-posedness and global attractor for wave equation with nonlinear damping and super-cubic nonlinearity",
  "authors": [
    "Cuncai Liu",
    "Fengjuan Meng",
    "Chang Zhang"
  ],
  "comment": "33 pages",
  "categories": [
    "math.AP",
    "math.DS"
  ],
  "abstract": "In the paper, we study the semilinear wave equation involving the nonlinear damping $g(u_t) $ and nonlinearity $f(u)$. Under the wider ranges of exponents of $g$ and $f$, the well-posedness of the weak solution is achieved by establishing a priori space-time estimates. Then, the existence of the global attractor in the naturally phase space $H^1_0(\\Omega)\\times L^2(\\Omega)$ is obtained. Moreover, we prove that the global attrator is regular, that is, the global attractor is a bounded subset of $(H^2(\\Omega)\\cap H^1_0(\\Omega))\\times H^1_0(\\Omega)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-11T16:14:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global attractor",
      "nonlinear damping",
      "super-cubic nonlinearity",
      "well-posedness",
      "semilinear wave equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}