{
  "abstract": "We study radially nonincreasing, positive blow-up solutions of a class of superlinear heat equations in the non-scale-invariant setting. This class contains nonlinearities with arbitrarily fast, super-exponential growth. Under suitable structural assumptions on the nonlinearity, we derive the sharp global blow-up profile in the original space-time variables. More precisely, for positive nonlinearities $f$ satisfying $$ \\lim_{X\\to \\infty}f'(X)G(X)= q\\ge1\\quad \\quad \\hbox{ where }\\quad\\quad G(X)=\\int_{X}^{\\infty}\\frac{ ds}{f(s)}<\\infty\\quad\\forall\\ X>0, $$ and assuming either the time monotonicity $u_t\\ge0$ holds or $q>\\frac{p_S}{p_S-1}$, we have $$ u(x,t)=(1+o(1))\\,G^{-1}\\bigg(T-t+\\frac{|x|^2}{4q|\\log |x|^2|}\\bigg), \\quad \\hbox{as $(x,t)\\to (0,T)$.} $$ This estimate in particular provides the sharp final space profile and the corresponding refined space-time profile. Moreover, our result recovers the universal structure of the global blow-up profile, given by the resolvent $G^{-1}$ of the associated ODE evaluated at a time-space building block, which only depends on the limit $q$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20013",
  "author_total": 1,
  "authors": [
    {
      "name": "Loth Damagui Chabi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d68w4n3jg6mw6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20013",
  "fulltext_url": null,
  "id": "d68w4n3jg6mw6",
  "issns": [],
  "landing_url": "https://hal.science/hal-05801881v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "hal",
      "0.math"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7222263067",
  "pdf_url": "https://hal.science/hal-05801881/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d68w4n3jg6mw6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:58Z",
      "native_id": "hal-05801881",
      "source": "hal",
      "url": "https://hal.science/hal-05801881v1"
    },
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.20013",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20013"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Refined blow-up behavior for semilinear heat equations with arbitrarily fast growing nonlinearities",
  "title_text": "Refined blow-up behavior for semilinear heat equations with arbitrarily fast growing nonlinearities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/d68w4n3jg6mw6",
  "venue": "HAL",
  "versions": []
}