{
  "abstract": "We study a nonlinear size-structured transport equation where the endogenous scalar output $E(t)=\\int_{l_0}^{l_m}χ(l)x(t,l)\\,dl$ feeds back into velocity and mortality. This principal-coefficient feedback precludes a semilinear perturbation framework. Freezing the feedback path yields a non-autonomous linear evolution, reducing the closed-loop problem to a scalar Volterra fixed point $E=\\mathcal K(E)$. Mass balance provides an intrinsic feedback interval, while a Bielecki-norm contraction ensures unique nonnegative weak solutions. Stationary equilibria satisfy a scalar closure equation $E=Φ(E)$. We prove uniqueness below the sharp margin $1-Φ'(E)>0$ and identify $Φ'(E)=1$ as a nondegenerate fold threshold. Linearization yields a finite-memory renewal equation with characteristic equation $\\mathcal E(λ)=1$, whose root set determines the feedback spectrum and stability. Finally, the stationary harvesting adjoint reduces to a rank-one perturbation formula. At zero discount, we establish the identity $\\mathcal E(0)=Φ'(E^*)=B(0)$, linking closure resonance, spectral crossing, and adjoint loop gain.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.02877",
  "author_total": 2,
  "authors": [
    {
      "name": "Jiguang Yu"
    },
    {
      "name": "Louis Shuo Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3bhcdwmgtj4ej.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.02877",
  "fulltext_url": null,
  "id": "3bhcdwmgtj4ej",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.02877",
  "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"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2739|Mathematical and Theoretical Epidemiology and Ecology Models"
    ]
  ],
  "openalex": "W7167644596",
  "pdf_url": "https://arxiv.org/pdf/2607.02877",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3bhcdwmgtj4ej.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2607.02877",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.02877"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Endogenous Feedback in Size-Structured Transport Equations",
  "title_text": "Endogenous Feedback in Size-Structured Transport Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/3bhcdwmgtj4ej",
  "venue": "arXiv",
  "versions": []
}