{
  "abstract": "We develop a rigorous analytical framework for a class of physiologically structured population models with two internal state variables, nonlocal ecological feedbacks, dynamic resources, inter-zone transfer, and selective harvesting. The full model is a coupled nonlinear PDE--ODE transport--renewal system with endogenous inflow at the recruitment boundary, a setting in which transport, nonlocal dependence, and boundary renewal interact at the same level. For this full nonautonomous multi-zone system, we prove finite-horizon well-posedness in a positive $L^{1}$-based state space, including global existence on arbitrary bounded time intervals, uniqueness, nonnegativity, and continuous dependence on initial data, environmental forcing, and harvesting effort. We then isolate an autonomous single-zone reduction at extinction and construct a positive compact next-generation operator on the recruit space. In a further nonlinear stationary reduction, we prove that supercriticality of the basic reproduction number $\\mathcal R_{0}>1$ yields existence of a nontrivial stationary state under a parametrized compact-operator hypothesis encoding density-dependent renewal feedback. Finally, for a finite-horizon harvest objective over a compact Lipschitz-regular admissible class, we establish existence of an optimal control. The results separate what can be proved for the full climate-explicit system from what can be justified only after autonomous reduction, thereby clarifying the mathematical scope of threshold and control theory for structured populations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00735",
  "author_total": 3,
  "authors": [
    {
      "name": "Jiguang Yu"
    },
    {
      "name": "Louis Shuo Wang"
    },
    {
      "name": "Ye Liang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4vadnmg9neswq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00735",
  "fulltext_url": null,
  "id": "4vadnmg9neswq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00735",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2609.00735",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4vadnmg9neswq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00735",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00735"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Rigorous Analysis of a Nonlocal Transport--Renewal System for Physiologically Structured Populations",
  "title_text": "Rigorous Analysis of a Nonlocal Transport--Renewal System for Physiologically Structured Populations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/4vadnmg9neswq",
  "venue": "arXiv",
  "versions": []
}