{
  "abstract": "We study the boundary stabilization of the variable-coefficient wave equation $u_{tt}=\\mathrm{div}(A\\nabla u)$ under mixed Zaremba boundary conditions in dimension $n\\ge 3$, the interface $\\Gamma$ being a compact submanifold of codimension two across which the boundary condition switches from Dirichlet to Neumann along a smooth boundary. We first establish an intrinsic edge decomposition: near $\\Gamma$, every strong solution reads $u=u_R+\\mathcal{K}_\\Gamma\\eta+w$, where $\\mathcal{K}_\\Gamma\\eta=\\chi(r)\\,r^{1/2}\\sin(\\theta/2)\\,\\omega(r\\Lambda)\\eta$ is defined through the functional calculus of the Laplacian of $\\Gamma$ and the remainder $w$ has vanishing renormalized traces on tubes around $\\Gamma$; this form is derived from the edge asymptotics of Dines–Harutjunjan–Schulze by strong convergence of traces, without identifying operators. We deduce the interface flux identity $\\lim_{\\varepsilon\\to 0} I_\\varepsilon=-\\frac{\\pi}{8}\\int_\\Gamma\\langle H,\\tau\\rangle_g\\,\\eta^2$ for the Riemannian multiplier $H$, and exponential energy decay with named constants under pointwise geometric assumptions, the Lyapunov closure proved in dimension two in a companion paper applying without change. We add a Riemannian star-shapedness criterion at the interface, a sufficient condition for the existence of an escape field $\\nabla_g f+K$ ($K$ Killing) compatible with the partition and, under strict transversality, the hidden regularity $\\eta\\in L^2(0,\\infty;L^2(\\Gamma))$ for all finite-energy data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Jean-Paul Bey"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0m4kqnnbptdaq.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "0m4kqnnbptdaq",
  "issns": [],
  "landing_url": "https://hal.science/hal-05828301v1",
  "language": "fr",
  "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": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-ap"
    ],
    [
      "hal",
      "1.math.math-oc"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05828301/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0m4kqnnbptdaq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:00Z",
      "native_id": "hal-05828301",
      "source": "hal",
      "url": "https://hal.science/hal-05828301v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ap",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-oc",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Interface identity and boundary stabilization of Zaremba problems in dimension n ≥ 3",
  "title_text": "Interface identity and boundary stabilization of Zaremba problems in dimension n ≥ 3",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:00Z",
  "url": "https://research.draconitic.com/paper/0m4kqnnbptdaq",
  "venue": "HAL",
  "versions": []
}