Waveguide with double threshold resonance at a simple threshold

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Waveguide with double threshold resonance at a simple threshold. / Nazarov, S. A.

In: Sbornik Mathematics, Vol. 211, No. 8, 08.2020, p. 1080-1126.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{458eb45f571244ac851ba87f0a4ab459,

title = "Waveguide with double threshold resonance at a simple threshold",

abstract = "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. ",

author = "Nazarov, {S. A.}",

year = "2020",

month = aug,

doi = "10.1070/SM9323",

language = "English",

volume = "211",

pages = "1080--1126",

journal = "Sbornik Mathematics",

issn = "1064-5616",

publisher = "Turpion Ltd.",

number = "8",

}

RIS

TY - JOUR

T1 - Waveguide with double threshold resonance at a simple threshold

AU - Nazarov, S. A.

PY - 2020/8

Y1 - 2020/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85095115724&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/edc0dd48-6f61-3eed-8a5e-c2c88afd8d90/

U2 - 10.1070/SM9323

DO - 10.1070/SM9323

M3 - Article

AN - SCOPUS:85095115724

VL - 211

SP - 1080

EP - 1126

JO - Sbornik Mathematics

JF - Sbornik Mathematics

SN - 1064-5616

IS - 8

ER -

ID: 71562047