{
  "abstract": "We study concentration expansions for the two-dimensional Keller-Segel free energy. The main result concerns semi-discrete quadratic optimal transport interpolations from a bounded compactly supported density to a prescribed finite atomic measure. Along these paths the energy admits a logarithmic expansion whose leading coefficient depends only on the masses assigned to the atoms. This coefficient captures the entropy-attraction balance associated with a prescribed finite splitting of the mass. Partial-concentration families with a diffuse remainder are analyzed by the same method. We also quantify how prescribed packet merging changes the leading coefficient, analyze critical profile relaxation and mesoscopic center coalescence, and construct explicit one-step JKO competitors.",
  "abstract_shown": true,
  "affiliations": [
    "Fudan Univ., Shanghai, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Jiaping Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f9vj31ns76h7k.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": "http://ejde.math.txstate.edu/Volumes/2026/79/abstr.html",
  "id": "f9vj31ns76h7k",
  "issns": [
    "1072-6691"
  ],
  "landing_url": "http://ejde.math.txstate.edu/Volumes/2026/79/abstr.html",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "lcc",
      "QA1-939"
    ]
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  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": "Texas State University",
  "ris": "https://research.draconitic.com/paper/f9vj31ns76h7k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T13:44:06Z",
      "native_id": "781f9441d3d84535a1585bfe1b17785a",
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      "url": "http://ejde.math.txstate.edu/Volumes/2026/79/abstr.html"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "lcc:QA1-939",
      "subfield": "general"
    }
  ],
  "title": "Multi-point concentration expansions for the two-dimensional Keller-Segel free energy",
  "title_text": "Multi-point concentration expansions for the two-dimensional Keller-Segel free energy",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T13:44:06Z",
  "url": "https://research.draconitic.com/paper/f9vj31ns76h7k",
  "venue": "Electronic Journal of Differential Equations",
  "versions": []
}