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<p>This paper obtains a&#xa0;sufficient condition for the existence of eigenoscillations in an acoustic cylindrical waveguide with a&#xa0;circular cross-section, inside which a&#xa0;thin-walled cross-shaped obstacle is placed. A continuous monotonic dependence of the smallest eigenvalue on the longitudinal size of the obstacle is proven.</p>

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On the Resonance on an Infinitely Thin Cross-Shaped Obstacle in a Circular Acoustic Waveguide

  • 期刊论文

  • 发表日期：

    2026年1月21日

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  • Igor Bimbaevich Yumov,
  • Tsyrenkhanda Zhembeevna Yumova

摘要

This paper obtains a sufficient condition for the existence of eigenoscillations in an acoustic cylindrical waveguide with a circular cross-section, inside which a thin-walled cross-shaped obstacle is placed. A continuous monotonic dependence of the smallest eigenvalue on the longitudinal size of the obstacle is proven.