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.
Keywords:
acoustic waveguide, double threshold resonance, almost standing waves, asymptotic analysis, near-threshold anomalies, weighted spaces with detached asymptotics.
\Bibitem{Naz20}
\by S.~A.~Nazarov
\paper Waveguide with double threshold~resonance at a~simple threshold
\jour Sb. Math.
\yr 2020
\vol 211
\issue 8
\pages 1080--1126
\mathnet{http://mi.mathnet.ru/eng/sm9323}
\crossref{https://doi.org/10.1070/SM9323}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4153723}
\zmath{https://zbmath.org/?q=an:1454.35063}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2020SbMat.211.1080N}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000586530900001}
\elib{https://elibrary.ru/item.asp?id=45208934}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85095115724}
Linking options:
https://www.mathnet.ru/eng/sm9323
https://doi.org/10.1070/SM9323
https://www.mathnet.ru/eng/sm/v211/i8/p20
This publication is cited in the following 5 articles:
S. A. Nazarov, “Gaps in the Spectrum of Thin Waveguides with Periodically Locally Deformed Walls”, Comput. Math. and Math. Phys., 64:1 (2024), 99
S. A. Nazarov, “Lakuny v spektre tonkikh volnovodov s periodicheski raspolozhennymi lokalnymi deformatsiyami stenok”, Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, 64:1 (2024)
S. A. Nazarov, K. M. Ruotsalainen, P. J. Uusitalo, “Scattering Coefficients and Threshold Resonances in a Waveguide with Uniform Inflation of the Resonator”, J Math Sci, 283:4 (2024), 617
S. A. Nazarov, “The preservation of threshold resonances and the splitting off of eigenvalues from the threshold of the continuous spectrum of quantum waveguides”, Sb. Math., 212:7 (2021), 965–1000
S. A. Nazarov, K. M. Ruotsalainen, P. I. Uusitalo, “Koeffitsienty rasseyaniya i porogovye rezonansy v volnovode pri ravnomernom rastyazhenii rezonatora”, Matematicheskie voprosy teorii rasprostraneniya voln. 51, Zap. nauchn. sem. POMI, 506, POMI, SPb., 2021, 175–209
Citation in format AMSBIB
Contact us: