{
  "abstract": "This paper study observability for the Dirichlet heat equation on a bounded interval with a real bounded potential depending on space and time. We prove an observability inequality from every measurable subset of spacetime with positive measure. The constant is uniform over potentials with a prescribed $L^\\infty$ bound. By duality, positive spacetime measure is equivalent to null controllability by square-integrable distributed controls. Controls can also be chosen bounded in time with values in $L^2$. If almost every spatial slice of the observation set has a fixed positive lower bound on its measure, the observability constant is bounded above by $C_0e^{C_1/T}$, uniformly in the locations of the slices. The proof combines observation estimates on finite-dimensional spaces transported by the evolution with decay estimates for the distance to those spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05704",
  "author_total": 1,
  "authors": [
    {
      "name": "Xiaomin Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1zpzs559pmx4v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05704",
  "fulltext_url": null,
  "id": "1zpzs559pmx4v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05704",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2207|Stability and Controllability of Differential Equations"
    ]
  ],
  "openalex": "W7220700152",
  "pdf_url": "https://arxiv.org/pdf/2610.05704",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1zpzs559pmx4v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05704",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05704"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Observability from Measurable Sets for One-Dimensional Heat Equations with Bounded Spacetime Potentials",
  "title_text": "Observability from Measurable Sets for One-Dimensional Heat Equations with Bounded Spacetime Potentials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/1zpzs559pmx4v",
  "venue": "arXiv",
  "versions": []
}