{
  "abstract": "In this paper, we study the Cauchy problems for a semilinear damped wave equation with a time-dependent coefficient for the damping term belonging to the class of non-effective damping terms with critical decay rates involving iterated logarithmic factors. As nonlinearities we consider both $|u|^p$ and $|u_t|^p$. Assuming nonnegative and compactly supported initial data, we establish the blow-up for weak solutions in the sub-Strauss range $1 < p \\leq p_{\\mathrm{Str}}(n)$ for the power of the nonlinear term $|u|^p$. The proof in the sub-critical case relies on an iteration frame for the space average of the solution, obtained by employing a time-dependent multiplier related to the coefficient of the damping term. On the other hand, in the limit case $p=p_{\\mathrm{Str}}(n)$, we work with solutions of the homogeneous equation with separated variables, and we investigate the properties of a fundamental system of solutions for the corresponding time-dependent ODE, in order to derive an iteration frame for a suitable weighted space average of the solution. Finally, for the derivative type nonlinearity $|u_t|^p$ we prove the blow-up of weak solutions in the sub-Glassey range $1 < p \\leq \\frac{n+1}{n-1}$ by using a comparison argument for a suitable time-dependent function associated with the corresponding local in time solution.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.14311",
  "author_total": 2,
  "authors": [
    {
      "name": "Wanderley Nunes do Nascimento"
    },
    {
      "name": "Alessandro Palmieri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9nv8rcdsgjh0y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.14311",
  "fulltext_url": null,
  "id": "9nv8rcdsgjh0y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.14311",
  "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.AP"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7203652373",
  "pdf_url": "https://arxiv.org/pdf/2608.14311",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9nv8rcdsgjh0y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2608.14311",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.14311"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Strauss and Glassey exponents for semilinear wave equations with a non-effective and not scattering producing damping",
  "title_text": "Strauss and Glassey exponents for semilinear wave equations with a non-effective and not scattering producing damping",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/9nv8rcdsgjh0y",
  "venue": "arXiv",
  "versions": []
}