{
  "abstract": "We investigate the fourth-order Jordan-Moore-Gibson-Thompson equation $$ u_{tttt}+αu_{ttt}+βu_{tt}-γΔu_{tt}-δΔu_{t}-\\varrho Δu=(f(u))_{ttt}+(f(u))_{tt} $$ under homogeneous Dirichlet boundary conditions in a smooth bounded domain $Ω\\subset \\mathbb{R}^n$ with $n\\leq 3$, where $α\\in \\mathbb{R}$ and $β,γ,δ,\\varrho>0$. First, for any suitably regular initial data and assuming that $f\\in C^4(\\mathbb{R})$ with $f(0)=0$, we prove that the corresponding initial-boundary value problem admits a unique maximal strong solution $u$ on $(0, T_{max})$. Second, by combining three time-integrated formulations with a series of resolvent-regularized energy estimates, we show that gradient blow-up is ruled out in the sense that \\begin{equation} \\tag{*} T_{max}<\\infty \\quad\\,\\, \\Rightarrow\\quad\\,\\, \\limsup_{t\\nearrow T_{max}}\\|u(\\cdot,t)\\|_{L^{\\infty}(Ω)}=\\infty. \\end{equation} Finally, assuming in addition that $f$ is convex and grows superlinearly in the sense that $$ f''(ξ)\\geq 0 \\;\\; \\mbox{ for all}\\;\\;ξ\\in\\mathbb{R}, \\qquad \\frac{f(ξ)}ξ\\rightarrow +\\infty\\;\\;\\mbox{ as}\\;\\; ξ\\rightarrow +\\infty , \\qquad \\int_{ξ_{0}}^{\\infty}\\frac{dξ}{f(ξ)}<\\infty \\;\\; \\mbox{ for some}\\;\\; ξ_{0}>0, $$ we employ the extensibility criterion (*) to prove that, for a suitable class of initial data, the solution blows up in finite time in the $L^\\infty$-norm. To the best of our knowledge, this provides the first rigorous description of finite-time blow-up for a genuinely nonlinear equation of fourth order in time.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33213",
  "author_total": 2,
  "authors": [
    {
      "name": "Tahir Boudjeriou"
    },
    {
      "name": "Filippo Dell'Oro"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bpk15351mverm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33213",
  "fulltext_url": null,
  "id": "bpk15351mverm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33213",
  "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"
    ],
    [
      "openalex",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7223812979",
  "pdf_url": "https://arxiv.org/pdf/2610.33213",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bpk15351mverm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.33213",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33213"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "$L^\\infty$ blow-up in the fourth-order Jordan-Moore-Gibson-Thompson equation",
  "title_text": "L^∞ blow-up in the fourth-order Jordan-Moore-Gibson-Thompson equation",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/bpk15351mverm",
  "venue": "arXiv",
  "versions": []
}