{
  "abstract": "We examine the inverse problem of recovering the potential term of an n-dimensional heat equation from a single time solution profile. We show that it is possible to uniquely determine this potential term via a stability inequality using solution measurements taken at a fixed time, assuming the potential is known within an arbitrary subdomain. The approach is based on the Carleman estimate. Additionally, we discuss the optimality of this type of observation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Nonlinear Analysis: Theory, Methods and Applications, 273",
  "arxiv": "2609.18814",
  "author_total": 2,
  "authors": [
    {
      "name": "Michel Cristofol"
    },
    {
      "name": "Alexandre Kawano"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/24n54t8c4jr6z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18814",
  "fulltext_url": null,
  "id": "24n54t8c4jr6z",
  "issns": [
    "0362-546X",
    "1873-5215"
  ],
  "landing_url": "https://hal.science/hal-05743036v1",
  "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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  "openalex": null,
  "pdf_url": "https://hal.science/hal-05743036/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-15",
  "publisher": "Elsevier",
  "ris": "https://research.draconitic.com/paper/24n54t8c4jr6z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:31Z",
      "native_id": "hal-05743036",
      "source": "hal",
      "url": "https://hal.science/hal-05743036v1"
    },
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18814",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18814"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Inverse problems for the diffusion equation with one time observation",
  "title_text": "Inverse problems for the diffusion equation with one time observation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/24n54t8c4jr6z",
  "venue": "Nonlinear Analysis: Theory, Methods and Applications",
  "versions": []
}