{
  "abstract": "We consider a inverse problem for a hyperbolic equation. The objective is to simultaneous recover both the spatially varying coefficient, whose square root represents the wave speed, and the initial displacement from a single pair of Dirichlet-Neumann Cauchy data. By introducing a suitable transformation and differentiating the resulting equation in time, we derive a coupled system for the differences of the unknown coefficient and initial displacement. Combining weighted energy estimates with Carleman estimates, we establish a Lipschitz stability estimate for both unknown quantities in appropriate Sobolev norms. The proof relies on a priori regularity assumptions, non-degeneracy conditions on the initial data, and structural inequalities controlling the interaction between the coefficient and initial-displacement differences. Our result extends coefficient-only stability results to a simultaneous coefficient--initial-displacement identification problem.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30767",
  "author_total": 2,
  "authors": [
    {
      "name": "Shiqi Ma"
    },
    {
      "name": "Qi Zhai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9qbmkyh51qn3b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30767",
  "fulltext_url": null,
  "id": "9qbmkyh51qn3b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30767",
  "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": "W7214590569",
  "pdf_url": "https://arxiv.org/pdf/2609.30767",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9qbmkyh51qn3b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30767",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30767"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Lipschitz stability in the simultaneous recovery of wave speed and initial source",
  "title_text": "Lipschitz stability in the simultaneous recovery of wave speed and initial source",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/9qbmkyh51qn3b",
  "venue": "arXiv",
  "versions": []
}