{
  "id": "2505.07255",
  "version": "v1",
  "published": "2025-05-12T06:10:38.000Z",
  "updated": "2025-05-12T06:10:38.000Z",
  "title": "Well-posedness and global attractor for wave equation with displacement dependent damping and super-cubic nonlinearity",
  "authors": [
    "Cuncai Liu",
    "Fengjuan Meng",
    "Chang Zhang"
  ],
  "categories": [
    "math.AP",
    "math.DS"
  ],
  "abstract": "This work investigates the semilinear wave equation featuring the displacement dependent term $\\sigma(u)\\partial_t u $ and nonlinearity $f(u)$. By developing refined space-time a priori estimates under extended ranges of the nonlinearity exponents with $\\sigma(u)$ and $f(u)$, the well-posedness of the weak solution is established. Furthermore, the existence of a global attractor in the naturally phase space $H^1_0(\\Omega)\\times L^2(\\Omega)$ is obtained. Moreover, the regularity of the global attractor is established, implying that it is a bounded subset of $(H^2(\\Omega)\\cap H^1_0(\\Omega))\\times H^1_0(\\Omega)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-12T06:10:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global attractor",
      "displacement dependent damping",
      "super-cubic nonlinearity",
      "well-posedness",
      "displacement dependent term"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}