{
  "abstract": "We establish a double-logarithmic stability estimate for the recovery of a time-dependent potential in the parabolic equation $(c^{-1}\\partial_t-Δ_g+q)u=0$ on a conformally transversally anisotropic manifold. The partial input--output map associates an initial state and lateral Dirichlet data supported in a prescribed open set with the terminal state and the Neumann trace on another open set. These sets contain the positive and negative boundary parts determined by a limiting Carleman weight, respectively. The measurement discrepancy is the operator norm of the difference of two such maps, whose range has improved Sobolev regularity. We prove stability under a uniform stability assumption for the attenuated geodesic ray transform on a family of non-tangential geodesics. This assumption is verified when the transversal manifold is simple and for regular families on certain non-simple manifolds. The proof uses Gaussian beam quasimodes with a uniform $O(h^{1/2})$ concentration estimate, geometric optics solutions obtained from boundary Carleman estimates, and stability of the geodesic ray transform for small attenuation. Quantitative analytic continuation for Hilbert-space-valued Fourier transforms and Sobolev interpolation yield the double-logarithmic modulus.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16759",
  "author_total": 3,
  "authors": [
    {
      "name": "Yujian Zheng"
    },
    {
      "name": "Zhiwen Duan"
    },
    {
      "name": "Shiqi Jing"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ddbftpeh9q1g6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16759",
  "fulltext_url": null,
  "id": "ddbftpeh9q1g6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16759",
  "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"
    ],
    [
      "openalex",
      "2610|Numerical methods in inverse problems"
    ]
  ],
  "openalex": "W7213417266",
  "pdf_url": "https://arxiv.org/pdf/2609.16759",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ddbftpeh9q1g6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.16759",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16759"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Double-logarithmic stability for a parabolic inverse problem on CTA manifolds",
  "title_text": "Double-logarithmic stability for a parabolic inverse problem on CTA manifolds",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/ddbftpeh9q1g6",
  "venue": "arXiv",
  "versions": []
}