{
  "abstract": "This paper investigates an inverse temporal source problem for a variable-exponent time-fractional diffusion equation with time-dependent diffusion coefficients. By the perturbation method, the model is equivalently transformed into a constant-order fractional diffusion equation with a convolution perturbation term. Existence, uniqueness, and energy estimates of strong and weak solutions to the forward problem are established, and for a separable source term the uniqueness and Lipschitz stability of the temporal source function are proved using local integral observations. A numerical reconstruction algorithm combining Tikhonov regularization with the conjugate gradient method is developed with a convergence error estimate, and numerical experiments verify its effectiveness and stability for different variable-exponent functions, noise levels and source functions. Since fractional advection--diffusion models describe the turbulent transport of airborne pollutants, the method is also applicable in atmospheric science for recovering the emission history of a pollution source from sparse measurements.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01019",
  "author_total": 3,
  "authors": [
    {
      "name": "Li Hu"
    },
    {
      "name": "Zhiyuan Li"
    },
    {
      "name": "Zhidong Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e776wmacq9ja7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01019",
  "fulltext_url": null,
  "id": "e776wmacq9ja7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01019",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01019",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e776wmacq9ja7.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01019",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01019"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Inverse source problem of variable-exponent time-fractional diffusion equations",
  "title_text": "Inverse source problem of variable-exponent time-fractional diffusion equations",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/e776wmacq9ja7",
  "venue": "arXiv",
  "versions": []
}