{
  "abstract": "Perhaps the most classical diffusion model for chemotaxis is the Keller-Segel system $$\\begin{aligned} \\left\\{ \\begin{aligned} u_t =&\\; \\Delta u - \\nabla \\cdot (u \\nabla v) \\quad {\\quad \\hbox {in } }\\mathbb {R}^2\\times (0,T),\\\\ v =&\\; (-\\Delta _{\\mathbb {R}^2})^{-1} u := \\frac{1}{2\\pi } \\int _{\\mathbb {R}^2} \\log \\frac{1}{|x-z|}\\,u(z,t) dz,\\\\&\\quad \\ u(\\cdot ,0) = u_0^{\\star } \\ge 0\\quad \\text {in } \\mathbb {R}^2. \\end{aligned} \\right. \\end{aligned}$$ u t = Δ u - ∇ · ( u ∇ v ) in R 2 × ( 0 , T ) , v = ( - Δ R 2 ) - 1 u : = 1 2 π ∫ R 2 log 1 | x - z | u ( z , t ) d z , u ( · , 0 ) = u",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY UK"
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  "article_type": null,
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  "author_total": 4,
  "authors": [
    {
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      ],
      "name": "Federico Buseghin"
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      "name": "Juan Dávila",
      "orcid": "0000-0002-7058-7930"
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    {
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      "name": "Manuel A. del Pino",
      "orcid": "0000-0001-6048-0657"
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    {
      "affs": [
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      "name": "Monica Musso",
      "orcid": "0000-0002-2564-0931"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/apjdxcb7k2fwb.bib",
  "cited_by": 11,
  "doi": "10.1007/s40818-026-00241-7",
  "fulltext_url": null,
  "id": "apjdxcb7k2fwb",
  "issns": [
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    "2524-5317"
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  "landing_url": "https://doi.org/10.1007/s40818-026-00241-7",
  "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": [
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  "openalex": "W4389363800",
  "pdf_url": null,
  "pmcid": "PMC13179901",
  "pmid": "42153167",
  "published": "2026-05-16",
  "publisher": "Springer Science+Business Media",
  "ris": "https://research.draconitic.com/paper/apjdxcb7k2fwb.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T13:20:42Z",
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      "url": "https://doi.org/10.1007/s40818-026-00241-7"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2611|Mathematical Biology Tumor Growth",
      "subfield": "general"
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  ],
  "title": "Existence of Finite Time Blow-Up in Keller-Segel System",
  "title_text": "Existence of Finite Time Blow-Up in Keller-Segel System",
  "type": "peer-reviewed",
  "updated_at": "2026-11-07T13:20:42Z",
  "url": "https://research.draconitic.com/paper/apjdxcb7k2fwb",
  "venue": "Annals of PDE",
  "versions": []
}