{
  "abstract": "In this paper, we investigate the spatial decay and asymptotic stability of forced waves for the Fisher-KPP equation in a shifting heterogeneous environment, focusing on the critical speed $c_*=2\\sqrt{r_+}$. Within the framework of regular variation, we establish a complete classification of critical wave tails in terms of the asymptotic behavior of the environmental deviation $r_+-r(z)$ as $z\\to+\\infty$. In each case, we derive precise spatial decay that characterize how the environmental tail modifies the leading-order decay of the wave at criticality. We further establish asymptotic stability estimates of forced waves. For initial data satisfying an exponentially weighted boundedness condition, we prove an $O(t^{-1/2})$ convergence rate in the uniform norm. Under stronger spatial decay assumptions on the weighted initial data, this rate improves to $O(t^{-1-σ/2})$, for $σ\\in[0,1]$, in both the uniform norm and a weighted norm. Moreover, no smallness assumption on the initial perturbations is needed for our results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30820",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhibao Tang"
    },
    {
      "name": "Lina Wang"
    },
    {
      "name": "Shi-Liang Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fms14djr6972p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30820",
  "fulltext_url": null,
  "id": "fms14djr6972p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30820",
  "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",
      "2739|Mathematical and Theoretical Epidemiology and Ecology Models"
    ]
  ],
  "openalex": "W7223365873",
  "pdf_url": "https://arxiv.org/pdf/2610.30820",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fms14djr6972p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30820",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30820"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Spatial Decay and Asymptotic Stability of Forced Waves at the Critical Speed for the Fisher-KPP Equation in a Shifting Environment",
  "title_text": "Spatial Decay and Asymptotic Stability of Forced Waves at the Critical Speed for the Fisher-KPP Equation in a Shifting Environment",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/fms14djr6972p",
  "venue": "arXiv",
  "versions": []
}