{
  "abstract": "In this article, we consider a wave equation on a bounded three-dimensional domain, featuring a degenerate nonlocal damping mechanism that depends on the system's energy and a source term with subquintic growth. This class of models is motivated by applications in optical physics. We establish global existence in the Shatah--Strichartz sense by combining Galerkin approximations with space-time Strichartz estimates on bounded domains. A central difficulty in the long-time analysis is the interplay between three-dimensional wave dynamics, nonlocal damping, and forcing terms that are not locally Lipschitz continuous. We prove the existence of a compact global attractor and derive an upper bound for its Kolmogorov $\\varepsilon$-entropy. In the non-degenerate damping case, assuming that the domain has a smooth, strictly convex boundary, we exploit the refined Strichartz estimates of Ivanovici {\\it et al.}~\\cite{Ivanovici-Lascar-Lebeau-Planchon-2023}, which yield, in particular, $u\\in L^3_tL^{18}_x$. Under the further assumption $f\\in C^2(\\mathbb R)$, this improved integrability allows us to establish quasi-stability of the associated dynamical system. Consequently, the global attractor has finite fractal dimension and higher regularity, and a generalized exponential attractor exists.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29778",
  "author_total": 3,
  "authors": [
    {
      "name": "Irena Lasiecka"
    },
    {
      "name": "Yanan Li"
    },
    {
      "name": "Vando Narciso"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/263m6pt5qa1ez.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29778",
  "fulltext_url": null,
  "id": "263m6pt5qa1ez",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29778",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7214290565",
  "pdf_url": "https://arxiv.org/pdf/2609.29778",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/263m6pt5qa1ez.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2609.29778",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29778"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Global Well-Posedness and Asymptotic Behavior of Energy-Damped Subquintic Wave Equations",
  "title_text": "Global Well-Posedness and Asymptotic Behavior of Energy-Damped Subquintic Wave Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/263m6pt5qa1ez",
  "venue": "arXiv",
  "versions": []
}