{
  "abstract": "This paper studies the vibration of a body with a hole (trap), which is caused by a plane acoustic wave. We assume that the body contains a periodic microstructure of small inclusions, which can partially reflect acoustic waves, and consider the scattering problem for the acoustic waves, which is modeled by an appropriate boundary value problem for the Helmholtz equation. Our goal is to describe the asymptotic behavior of the spectrum of this boundary value problem as the period of the microstructure and the diameter of the hole tend to zero. The scattering frequencies are characterized by the poles of the analytic continuation of the resolvent of the corresponding boundary value problem.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Differential Equations, Faculty of Mechanics and Mathematics, M.V. Lomonosov Moscow State University, Leninskie Gory, 1, Moscow 119991, Russia",
    "Department of Mathematical Analysis, Faculty of Physics and Mathematics, Akmulla Bashkir State Pedagogical University, Ufa 450077, Russia",
    "Faculty of Engineering Science and Technology, UiT The Arctic University of Norway, P.O. Box 385, 8505 Narvik, Norway",
    "Higher School of Modern Mathematics, Moscow Institute of Physics and Technology, 1 Klimentovski per., Moscow 115184, Russia"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Gregory A. Chechkin",
      "orcid": "0000-0002-7654-5803"
    },
    {
      "affs": [
        1
      ],
      "name": "Rustem R. Gadyl’shin"
    },
    {
      "affs": [
        2,
        3
      ],
      "name": "Andrey L. Piatnitski",
      "orcid": "0000-0002-9874-6227"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5z2jycjeekr87.bib",
  "cited_by": 0,
  "doi": "10.3390/math14203803",
  "fulltext_url": null,
  "id": "5z2jycjeekr87",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/20/3803",
  "language": null,
  "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": [
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7223067326",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/5z2jycjeekr87.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14203803",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/20/3803"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Spectral Theory in Mathematical Physics",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "On the Frequencies of Scattering on Traps with Micro-Inhomogeneous Structures—Helmholtz Resonators",
  "title_text": "On the Frequencies of Scattering on Traps with Micro-Inhomogeneous Structures—Helmholtz Resonators",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/5z2jycjeekr87",
  "venue": "Mathematics",
  "versions": []
}