{
  "id": "2307.15789",
  "version": "v1",
  "published": "2023-07-28T20:03:48.000Z",
  "updated": "2023-07-28T20:03:48.000Z",
  "title": "Existence and regularity of pullback attractors for nonclassical non-autonomous diffusion equations with delay",
  "authors": [
    "Bin Yang",
    "Yuming Qin",
    "Alain Miranville",
    "Ke Wang"
  ],
  "comment": "30 pages",
  "categories": [
    "math.AP",
    "math.DS"
  ],
  "abstract": "In this paper, we consider the asymptotic behavior of weak solutions for non-autonomous diffusion equations with delay in time-dependent spaces when the nonlinear function $f$ is critical growth, the delay term $g(t, u_t)$ contains some hereditary characteristics and the external force $h \\in L_{l o c}^{2}\\left(\\mathbb{R} ; L^{2}(\\Omega)\\right)$. Firstly, we prove the well-posedness of solutions by using the Faedo-Galerkin approximation method. Then after a series of elaborate energy estimates and calculations, we establish the existence and regularity of pullback attractors in time-dependent spaces $C_{\\mathcal{H}_{t}(\\Omega)}$ and $C_{\\mathcal{H}^{1}_{t}(\\Omega)}$ respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-28T20:03:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35B41",
      "35B65",
      "35K57"
    ],
    "keywords": [
      "nonclassical non-autonomous diffusion equations",
      "pullback attractors",
      "regularity",
      "time-dependent spaces",
      "elaborate energy estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}