{
  "abstract": "We study a nonlocal Fisher--KPP equation on the real line with compactly supported initial data. The reaction satisfies $f(s)\\le f^{\\prime}(0)s$ for $0\\le s\\le1$, with a power bound on $f^{\\prime}(0)s-f(s)$ near zero. For continuous even probability kernels $J$ comparable to $|x|^{-γ}$, $γ>1$, we prove a global two-sided estimate and locate every fixed level set with a bounded error in $\\log|x|$. The propagation scale is $\\exp(f'(0)t/γ)$ for every $γ>1$. This differs sharply from the free-boundary propagation studied by Du and Ni \\cite{DuNiJEMS}. For polynomial kernel tails, spreading in their model has linear, algebraic or $t\\log t$ growth. We also obtain arrival-time and weighted-integral estimates and identify a spatial tail coefficient when $|x|^γJ(x)$ has a positive limit.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30986",
  "author_total": 1,
  "authors": [
    {
      "name": "Yuanyang Hu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2m6zmqdpkf07z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30986",
  "fulltext_url": null,
  "id": "2m6zmqdpkf07z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30986",
  "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": "W7223342382",
  "pdf_url": "https://arxiv.org/pdf/2610.30986",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2m6zmqdpkf07z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30986",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30986"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Nonlocal Fisher--KPP propagation with heavy tails",
  "title_text": "Nonlocal Fisher--KPP propagation with heavy tails",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/2m6zmqdpkf07z",
  "venue": "arXiv",
  "versions": []
}