{
  "abstract": "We consider the Cauchy problem for semilinear classical damped wave equations with general nonnegative nondecreasing nonlinearities, without imposing a modulus-of-continuity structure or convexity. A Dini-type integral condition expressed directly in terms of the nonlinearity gives small data global in-time existence and extends the nonlinear framework of Ebert--Girardi--Reissig [Math. Ann. 378 (2020), 1311--1326]. When this Dini-type integral diverges and the effective total mass of the initial data is positive, convergence of the Keller--Osserman tail integral is necessary and sufficient for finite-time blow-up of the maximal mild Sobolev solution, particularly, divergence of the tail integral gives global grow-up. The resulting integral criteria distinguish the contributions of the nonlinearity near zero and at infinity in governing small data global in-time existence with diffusion decay, global grow-up, and finite-time blow-up.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27862",
  "author_total": 1,
  "authors": [
    {
      "name": "Wenhui Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4jhvg92t4vzm6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27862",
  "fulltext_url": null,
  "id": "4jhvg92t4vzm6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27862",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7214225391",
  "pdf_url": "https://arxiv.org/pdf/2609.27862",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4jhvg92t4vzm6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2609.27862",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27862"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Critical semilinear damped wave equations beyond moduli of continuity",
  "title_text": "Critical semilinear damped wave equations beyond moduli of continuity",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/4jhvg92t4vzm6",
  "venue": "arXiv",
  "versions": []
}