{
  "abstract": "We are concerned with the following partial differential equations arising from urban crime modeling: \\begin{equation} \\label{main} \\begin{cases} u_t = Δu - χ\\nabla \\cdot \\left( u \\dfrac{\\nabla v}{v} \\right) - uv + B_1 + ru - μu^2, \\\\[4pt] v_t = Δv - v + uv + B_2, \\end{cases} \\end{equation} under no-flux boundary conditions in a smoothly bounded domain $Ω\\subset \\mathbb{R}^n$ with $n \\geq 2$, where $χ$, $r$, and $μ$ are positive constants. It is shown in this paper that if the nonnegative source terms $B_1$ and $B_2$ are sufficiently regular and \\begin{equation*} μ> \\frac{3}{n} + \\frac{1}{n}\\left( χn + \\frac{n(χ(n-1)-2)^2}{4(n-1)} \\right)^{\\frac{n+1}{n}} \\cdot \\left( \\frac{(2n+\\sqrt{n})^2}{2n-1} \\right)^{\\frac{1}{n}} + n^{12n+3}, \\end{equation*} then the system \\eqref{main} with suitably regular initial data possesses a global classical solution. Moreover, under the assumption that \\begin{equation*} \\label{cond.B2} \\inf_{t>0} \\int_ΩB_2(\\cdot,t) > 0, \\end{equation*} the solutions are uniformly bounded in time.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23373",
  "author_total": 1,
  "authors": [
    {
      "name": "Minh Le"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/52xw574qvc1c9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23373",
  "fulltext_url": null,
  "id": "52xw574qvc1c9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23373",
  "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"
    ],
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      "openalex",
      "2611|Mathematical Biology Tumor Growth"
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  "openalex": "W7214043337",
  "pdf_url": "https://arxiv.org/pdf/2609.23373",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/52xw574qvc1c9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23373",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23373"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Global existence of classical solutions to a system modeling propagation of urban crime with quadratic logistic damping",
  "title_text": "Global existence of classical solutions to a system modeling propagation of urban crime with quadratic logistic damping",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/52xw574qvc1c9",
  "venue": "arXiv",
  "versions": []
}