{
  "abstract": "In this paper, we study the optimal control of a phase field tumor growth model of Cahn--Hilliard type with possibly singular potential in which the often assumed parabolic relaxation of the chemical potential is replaced by a hyperbolic one. We investigate the asymptotic behavior of the control problem as the relaxation parameter $\\,α\\,$ approaches zero. It is shown that the corresponding state and adjoint state variables of the relaxed problem converge in a suitable sense to their counterparts for the unrelaxed regime where $α=0$. Also, weak limits of optimal controls for the relaxed problem can be shown to be optimal controls for the unrelaxed case. Moreover, every fixed optimal control $\\,u^*\\,$ for the unrelaxed system turns out to be the limit of a family $\\{u^*_α\\}_{α>0}$ of minimizers of suitable optimal control problems for the relaxed systems, where the original cost functional is replaced by the so-called ``adapted'' cost functional. It is also shown that the variational inequalities satisfied by $u^*_α$, which constitute the first-order necessary optimality conditions of the relaxed problems with adapted cost functional, converge to the corresponding variational inequality fulfilled by $u^*$ for the unrelaxed problem with the original (nonadapted) cost functional.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04380",
  "author_total": 3,
  "authors": [
    {
      "name": "Pierluigi Colli"
    },
    {
      "name": "Elisabetta Rocca"
    },
    {
      "name": "Jürgen Sprekels"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2j7d50hcj9zpj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04380",
  "fulltext_url": null,
  "id": "2j7d50hcj9zpj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04380",
  "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": "W7220729654",
  "pdf_url": "https://arxiv.org/pdf/2610.04380",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2j7d50hcj9zpj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.04380",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04380"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Asymptotic analysis of an optimal control problem for a phase field tumor growth model with hyperbolic relaxation of the chemical potential",
  "title_text": "Asymptotic analysis of an optimal control problem for a phase field tumor growth model with hyperbolic relaxation of the chemical potential",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/2j7d50hcj9zpj",
  "venue": "arXiv",
  "versions": []
}