{
  "abstract": "Continuum angiogenesis systems often use local endothelial or vessel density as an oxygen-delivery proxy without distinguishing structurally formed vessels from pressure-supported vascular function. We formulate a two-dimensional model in which lumenized density determines a normalized nonlocal conductivity, a globally solved pressure field, and a flow-functional density that gates oxygen delivery and vessel regression. For fixed positive regularization parameters and signal relaxation times, we prove Lipschitz stability of the pressure--perfusion map and global bounded weak solvability; strong vessel compactness follows from a nonlocal ordinary differential equation stability estimate rather than spatial smoothing. As the oxygen and vascular endothelial growth factor timescales vanish simultaneously, weak solutions converge along a subsequence to a parabolic--elliptic--ordinary differential equation system, with both fast fields converging strongly in \\(L^2(0,T;H^1)\\). A locally frozen one-dimensional reduction admits monotone fronts precisely at or above the threshold \\(B+2\\sqrt{DR}\\) for \\(B\\geq-\\sqrt{DR}\\) and \\(-DR/B\\) otherwise. Finite-volume experiments verify the analytical mechanisms and show that equal-mass vessel fields can generate distinct functional masses and oxygenation levels.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13753",
  "author_total": 2,
  "authors": [
    {
      "name": "Jiguang Yu"
    },
    {
      "name": "Louis Shuo Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f8pzsz8nnket4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13753",
  "fulltext_url": null,
  "id": "f8pzsz8nnket4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13753",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2611|Mathematical Biology Tumor Growth"
    ]
  ],
  "openalex": "W7213355239",
  "pdf_url": "https://arxiv.org/pdf/2609.13753",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f8pzsz8nnket4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13753",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13753"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A Nonlocal Perfusion-Gated Angiogenesis System: Global Weak Solutions, Fast-Signal Limits, and Invasion Fronts",
  "title_text": "A Nonlocal Perfusion-Gated Angiogenesis System: Global Weak Solutions, Fast-Signal Limits, and Invasion Fronts",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/f8pzsz8nnket4",
  "venue": "arXiv",
  "versions": []
}