{
  "abstract": "We consider polynomial nonlinear PDEs on compact manifolds with finite-dimensional forcing terms. We provide necessary and sufficient conditions, such that the forcing trough the nonlinear dynamics attains a dense subspace on manifolds with and without boundary. Our key argument is the Nachbin’s theorem, which is an analogue of the well-known Stone-Weierstrass the- orem in differentiable spaces. As applications, we prove small-time approximate controllability by additive finite-dimensional controls, topological irreducibility and almost sure unboundedness of Sobolev norms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29914",
  "author_total": 3,
  "authors": [
    {
      "name": "Rémi Buffe"
    },
    {
      "name": "Alessandro Duca"
    },
    {
      "name": "Hugo Parada"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7vjntn78qz13p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29914",
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  "id": "7vjntn78qz13p",
  "issns": [],
  "landing_url": "https://hal.science/hal-05800260v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
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      "arxiv",
      "math.OC"
    ],
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    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
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  ],
  "openalex": "W7223073216",
  "pdf_url": "https://hal.science/hal-05800260/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7vjntn78qz13p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:00Z",
      "native_id": "hal-05800260",
      "source": "hal",
      "url": "https://hal.science/hal-05800260v1"
    },
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29914",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29914"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Saturation on compact manifolds via Stone-Weierstrass type theorem, and forced nonlinear PDEs",
  "title_text": "Saturation on compact manifolds via Stone-Weierstrass type theorem, and forced nonlinear PDEs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/7vjntn78qz13p",
  "venue": "HAL",
  "versions": []
}