Waveguide with double threshold~resonance at a~simple threshold
Sbornik. Mathematics, Tome 211 (2020) no. 8, pp. 1080-1126
Voir la notice de l'article provenant de la source Math-Net.Ru
A threshold resonance generated by an almost standing wave occurring at a threshold — a solution of the problem that do not decay at infinity, but rather stabilizes there — brings about various anomalies in the diffraction pattern at near-threshold frequencies. Examples when a simple threshold resonance occurs or does not occur are trivial. For the first time an acoustic waveguide (the Neumann spectral problem for the Laplace operator) of a special shape is constructed in which there is a maximum possible number (namely two) of linearly independent almost standing waves at a threshold (equal to a simple eigenvalue of the model problem on the cross-section of the cylindrical outlets to infinity). Effects in the scattering problem for acoustic waves, which are caused by these standing waves are discussed.
Bibliography: 54 titles.
Keywords:
acoustic waveguide, double threshold resonance, almost standing waves, asymptotic analysis, near-threshold anomalies, weighted spaces with detached asymptotics.
@article{SM_2020_211_8_a1,
author = {S. A. Nazarov},
title = {Waveguide with double threshold~resonance at a~simple threshold},
journal = {Sbornik. Mathematics},
pages = {1080--1126},
publisher = {mathdoc},
volume = {211},
number = {8},
year = {2020},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2020_211_8_a1/}
}
S. A. Nazarov. Waveguide with double threshold~resonance at a~simple threshold. Sbornik. Mathematics, Tome 211 (2020) no. 8, pp. 1080-1126. http://geodesic.mathdoc.fr/item/SM_2020_211_8_a1/