{
  "abstract": "We resolve the Hamel-Nadirashvili conjecture, which concerns the classification of all [0,1]-valued entire solutions of Fisher-KPP equations with concave C^2 reaction terms in arbitrary space dimension. We prove that every such solution is a C_{loc}^{1,2} limit of solutions generated by finitely many planar traveling fronts, possibly together with a spatially homogeneous solution. Our approach reveals an ordered linear structure underlying the nonlinear solution space, leading to a critical-subcritical spectral decomposition. The proof combines linear reconstruction of subcritical approximants with a measure representation (a kind of nonlinear Martin representation) of critical solutions, obtained through small-amplitude asymptotics and comparison with a radially symmetric entire solution.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27896",
  "author_total": 3,
  "authors": [
    {
      "name": "Hongjun Guo"
    },
    {
      "name": "Kelei Wang"
    },
    {
      "name": "Maolin Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0zr4qm25m5m0q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27896",
  "fulltext_url": null,
  "id": "0zr4qm25m5m0q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27896",
  "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",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7223147710",
  "pdf_url": "https://arxiv.org/pdf/2610.27896",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0zr4qm25m5m0q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27896",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27896"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "The Hamel-Nadirashvili conjecture for the Fisher-KPP equation",
  "title_text": "The Hamel-Nadirashvili conjecture for the Fisher-KPP equation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/0zr4qm25m5m0q",
  "venue": "arXiv",
  "versions": []
}