{
  "abstract": "We consider the nonlinear Hardy-Hénon parabolic equation $ u_t=Δu+|x|^l|u|^αu,$ $t>0,$ $x\\in\\mathbb{R}^N$ or $x\\in\\mathbb{R}^N\\setminus\\{0\\}$, with $N\\ge1$, $l>-\\min\\{2,N\\}$, $α>0$, with nonnegative initial datum $u_0$. We first establish new criteria for finite-time blow-up. We then derive optimal upper bounds for the life-span $T_{\\max}(λφ)$ of solutions arising from the initial datum $u_0=λφ$. These estimates establish a precise dependence of $T_{\\max}(λφ)$ on both the initial profile $φ$ and the parameter $λ$ in the small and large-amplitude regimes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08662",
  "author_total": 2,
  "authors": [
    {
      "name": "Byrame Ben Slimene"
    },
    {
      "name": "Slim Tayachi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0vpgs43mghk5g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08662",
  "fulltext_url": null,
  "id": "0vpgs43mghk5g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08662",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08662",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0vpgs43mghk5g.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:07Z",
      "native_id": "2611.08662",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08662"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Blow-Up and Life-Span for Nonlinear Hardy-Hénon Parabolic Equations",
  "title_text": "Blow-Up and Life-Span for Nonlinear Hardy-Hénon Parabolic Equations",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:07Z",
  "url": "https://research.draconitic.com/paper/0vpgs43mghk5g",
  "venue": "arXiv",
  "versions": []
}