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We study wave diffraction at near-threshold frequencies in an acoustic waveguide with a cross-wall that has a small aperture of diameter ε > 0. We describe the effects of almost complete reflection or transmission of waves related to the classical Vainstein anomaly and the presence of almost standing waves for the threshold value Λk of the spectral parameter λ in continuous spectrum. The greatest attention is paid to analyzing the range λε = Λk + ε2μ2 of the spectral parameter with μ ≤ μ0, which generates scattering coefficients depending on μ > 0 and presents the greatest difficulties in constructing and justifying the asymptotics. Almost complete reflection and transmission correspond to the cases of going away from the threshold (as μ → +∞) and approaching it (as μ → +0) characterized by simpler asymptotics.
Original language | English |
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Pages (from-to) | 85-101 |
Number of pages | 17 |
Journal | Siberian Mathematical Journal |
Volume | 59 |
Issue number | 1 |
Early online date | 9 Mar 2018 |
DOIs | |
State | Published - 2018 |
ID: 40973988