{
  "abstract": "We consider a family of semilinear parabolic equations with homogeneous Neumann boundary conditions on a family of varying non-smooth domains $\\{Ω_μ\\}_{μ\\in Λ} \\subset \\mathbb{R}^n $. Assuming only that the domains have uniformly bounded volumes, bounded away from zero, and satisfy a uniform Jones condition, together with the usual structural requirements on the linear and nonlinear terms, we establish the well-posedness of the problem in an appropriate scale of fractional Banach spaces and prove the existence of global attractors. Using a Moser-Alikakos bootstrap iteration in conjunction with the uniform Gronwall lemma and the uniform properties of the Jones extension operator, we show that bounded sets of $L^{q}(Ω_μ)$ are absorbed, in finite time and uniformly in $μ$, into a fixed ball of $L^\\infty(Ω_μ)$; the iteration uses only first-order Sobolev embeddings, which is what makes it available on domains where the domain of the elliptic operator is not contained in $H^{2}$. Finally, assuming the volume convergence of the domains, $|Ω_μ\\triangle Ω_0| \\to 0$, we construct a framework of connecting maps and prove that the family of attractors is upper semicontinuous at $μ= 0$ in $L^2(Ω_μ)$ and hence, by interpolation, in $H^s(Ω_μ)$ for every $s<1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.08061",
  "author_total": 1,
  "authors": [
    {
      "name": "Antonio L. Pereira"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/10ksb0anefc1q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.08061",
  "fulltext_url": null,
  "id": "10ksb0anefc1q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.08061",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "openalex",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7167938674",
  "pdf_url": "https://arxiv.org/pdf/2607.08061",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/10ksb0anefc1q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2607.08061",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.08061"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Uniform $L^{\\infty}$-Boundedness of Global Attractors for Reaction-Diffusion Equations with Neumann boundary condition in Uniformly Perturbed Non-Smooth Domains",
  "title_text": "Uniform L^∞-Boundedness of Global Attractors for Reaction-Diffusion Equations with Neumann boundary condition in Uniformly Perturbed Non-Smooth Domains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/10ksb0anefc1q",
  "venue": "arXiv",
  "versions": []
}