{
  "abstract": "In this paper, we study an integral equation of Landau-Lifschitz-type involving the Riesz potential $$ u(x)=\\ell+C_*\\int_{\\mathbb{R}^n}\\frac{u(y)(|\\nabla u(y)|^{2}+|u_k(y)|^2)-u_k(y)e_k}{|x-y|^{n-α}}dy, $$ where $\\ell \\in \\mathbb{R}^k$ is a constant vector, $C_* \\neq 0$ is a constant, $u\\colon\\mathbb{R}^n \\to \\mathbb{S}^{k-1}:=\\{u=(u_1,u_2,\\cdots,u_k) \\in {\\mathbb{R}^{k}};|u|=1\\}$, $k \\geq 1$, $n \\geq 2$, and $0<α<n$. We provide a decay rate at which $|u_k|$ converges to zero under some mild conditions. This argument still works for the Ginzburg-Landau-type integral equation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.07391",
  "author_total": 1,
  "authors": [
    {
      "name": "Tiantian Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b5154pxyhvjya.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.07391",
  "fulltext_url": null,
  "id": "b5154pxyhvjya",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.07391",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.07391",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b5154pxyhvjya.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.07391",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.07391"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Asymptotic behavior of an integral equation of Landau-Lifschitz type",
  "title_text": "Asymptotic behavior of an integral equation of Landau-Lifschitz type",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:47Z",
  "url": "https://research.draconitic.com/paper/b5154pxyhvjya",
  "venue": "arXiv",
  "versions": []
}