{
  "id": "2303.14875",
  "version": "v1",
  "published": "2023-03-27T01:52:31.000Z",
  "updated": "2023-03-27T01:52:31.000Z",
  "title": "Regularity of pullback attractors for nonclassical diffusion equations with delay",
  "authors": [
    "Yuming Qin",
    "Qitao Cai",
    "Ming Mei",
    "Ke Wang"
  ],
  "categories": [
    "math.AP",
    "math.DS"
  ],
  "abstract": "In this paper, we mainly study the regularity of pullback $\\mathcal{D}$-attractors for a nonautonomous nonclassical diffusion equation with delay term $b(t,u_t)$ which contains some hereditary characteristics. Under a critical nonlinearity $f$, a time-dependent force $g(t,x)$ with exponential growth and a delayed force term $b(t,u_t)$, we prove that there exists a pullback $\\mathcal{D}$-attractor $\\mathcal{A}=\\{A(t):t \\in \\mathbb{R}\\}$ in $\\mathbb{K}^1=H_0^1(\\Omega) \\times L^2((-h,0);L^2(\\Omega))$ to problem \\eqref{ine01} and for each $t \\in \\mathbb{R}$, $A(t)$ is bounded in $\\mathbb{K}^2=H^2(\\Omega) \\cap H_0^1(\\Omega) \\times L^2((-h,0);L^2(\\Omega))$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-27T01:52:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "pullback attractors",
      "regularity",
      "nonautonomous nonclassical diffusion equation",
      "hereditary characteristics",
      "time-dependent force"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}