{
  "annotation_id": "ba24dba1-15ca-4bf0-8216-7319996f18c7",
  "date_created": "2026-02-17T05:53:08.809000Z",
  "date_modified": "2026-02-17T05:53:08.809000Z",
  "file_hash": "bfa0a5fdb429dacea4071f3364de22837f928776f4007d1421f61408d15b1ac2",
  "private": false,
  "record": {
    "abstract": "This article aims to study the long-time dynamics of the linear viscoelastic plate equation $\\displaystyle{u_{tt}+\\Delta^2 u-\\int_{\\tau}^tg(t-s)\\Delta^2u(s)ds=0}$ subject to nonlinear and nonlocal boundary conditions. This model, with $\\tau=0$, was first considered by Cavalcanti (Discrete Contin. Dyn. Syst., 8(3), 675-695, 2002), where results of global existence and uniform decay rates of energy have been established. In this work, by taking $\\tau=-\\infty$, and considering the autonomous equivalent problem we prove that the dynamical system $(\\mathcal{H},S_t)$ generated by the weak solutions has a compact global attractor $\\mathfrak{A}$ (in the topology of the weak phase space $\\mathcal{H}$), which in subcritical case has finite dimension and smoothness. Furthermore, when the force follows the {\\it Hook Law}, we prove that $(\\mathcal{H},S_t)$ possesses a (generalized) fractal exponential attractor $\\mathfrak{A}_{\\exp}$ with finite dimension in a space $\\widetilde{\\mathcal{H}}\\supset\\mathcal{H}$.",
    "arxiv_id": "2601.06414",
    "authors": [
      "Linfang Liu",
      "Vando Narciso",
      "Zhijian Yang"
    ],
    "categories": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "title": "Dynamics for a viscoelastic beam equation with past history and nonlocal boundary dissipation",
    "url": "https://arxiv.org/abs/2601.06414",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "87c35dd9-307a-4760-9969-2852fb660d4d",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}