{
  "abstract": "We consider the quasilinear Hardy-Hénon equation $$ u_t=Δu^m+|x|^σu^p, \\quad (x,t)\\in\\mathbb{R}^N\\times(0,T), $$ in the range of exponents and dimension $$ N\\geq3, \\quad σ\\in(-2,\\infty), \\quad m>1, \\quad p>p_S(σ)=\\frac{m(N+2σ+2)}{N-2}. $$ We establish sharp ranges of exponents $(m,p,σ)$ guaranteeing existence of \\emph{peaking solutions} in backward self-similar form $$ u(x,t)=(T-t)^{-α}f(|x|(T-t)^{-β}). $$ By peaking solutions we understand solutions blowing up at a finite time $T\\in(0,\\infty)$ but allowing for a continuation after the blow-up time. As a remarkable outcome, a number of ranges of exponents $σ$ and $m$ for which peaking solutions exist for any $p>p_S(σ)$ are deduced, contrasting to the previously considered exponent $σ=0$, where a Lepin-type critical exponent $p_L$ provides an upper bound for $p$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.32304",
  "author_total": 3,
  "authors": [
    {
      "name": "Razvan Gabriel Iagar"
    },
    {
      "name": "Ariel Sánchez"
    },
    {
      "name": "Erik Sarrión-Pedralva"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9ryk9wkgv6cjx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.32304",
  "fulltext_url": null,
  "id": "9ryk9wkgv6cjx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.32304",
  "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",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7223677905",
  "pdf_url": "https://arxiv.org/pdf/2610.32304",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9ryk9wkgv6cjx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:19Z",
      "native_id": "2610.32304",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.32304"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Peaking self-similar solutions and continuation after blow-up for a quasilinear Hardy-Hénon equation",
  "title_text": "Peaking self-similar solutions and continuation after blow-up for a quasilinear Hardy-Hénon equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/9ryk9wkgv6cjx",
  "venue": "arXiv",
  "versions": []
}