{
  "abstract": "We study an optimal control problem for a two-equations Keller-Segel system on a bounded domain with Neumann boundary conditions, where the chemotactic sensitivity is modulated by a control $f(x,t)$ acting on the taxis flux $\\nabla\\!\\cdot(f\\,u\\,\\nabla v)$. We prove the well-posedness of the state equation under low regularity assumptions. The analysis is based on the study of an $\\varepsilon$-regularized problem, the application of Schauder's fixed point theorem, $\\varepsilon$-independent, positivity and a priori estimates, the passage to the limit as $\\varepsilon \\to 0$, and a uniqueness argument. For a cost functional combining trajectory tracking, taxis penalization, control regularization, and terminal objectives, we establish the existence of optimal controls and derive the first-order optimality conditions through a Lagrange multiplier framework, leading to an adjoint system and a variational inequality for the optimal control. A numerical scheme based on spline collocation in space and Runge-Kutta time-stepping is set and implemented. Numerical experiments are performed to simulate the free and controlled dynamics in conservative and non-conservative cases.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18030",
  "author_total": 3,
  "authors": [
    {
      "name": "Yacouba Simpore"
    },
    {
      "name": "Mahamadi Warma"
    },
    {
      "name": "Luis P. Yapu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fdcmse775p0yk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18030",
  "fulltext_url": null,
  "id": "fdcmse775p0yk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18030",
  "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",
      "2611|Mathematical Biology Tumor Growth"
    ]
  ],
  "openalex": "W7213525758",
  "pdf_url": "https://arxiv.org/pdf/2609.18030",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fdcmse775p0yk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18030",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18030"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Optimal control via chemotactic sensitivity of a logistic Keller-Segel model",
  "title_text": "Optimal control via chemotactic sensitivity of a logistic Keller-Segel model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/fdcmse775p0yk",
  "venue": "arXiv",
  "versions": []
}