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Sbornik: Mathematics, 2014, Volume 205, Issue 7, Pages 953–982
DOI: https://doi.org/10.1070/SM2014v205n07ABEH004405 (Mi sm8286) 		 
This article is cited in 34 scientific papers (total in 34 papers)

Umov-Mandelshtam radiation conditions in elastic periodic waveguides

S. A. Nazarovab

a Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, St. Petersburg
b St. Petersburg State University, Department of Mathematics and Mechanics
English version PDF (743 kB) Citations (34)
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DOI: https://doi.org/10.1070/SM2014v205n07ABEH004405
Abstract: We study settings of the problem of elasticity theory on wave propagation in an elastic periodic waveguide with radiation conditions at infinity. We present a mathematical theory for energy radiation conditions based on Mandelshtam's energy principle and the Umov-Poynting vector, as well as using the technique of weighted spaces with detached asymptotics and the energy transfer symplectic form. We establish that in a threshold situation, that is, when standing and polynomial elastic Floquet waves appear, the well-known limiting absorption principle, in contrast to the energy principle that is being applied, cannot identify the direction of the wave's motion.
Bibliography: 37 titles.
Keywords: elastic periodic waveguide, Mandelshtam's energy radiation condition, Umov-Poynting vector, energy transfer symplectic form.
Funding agency Grant number
Russian Foundation for Basic Research 12-01-00348
Received: 26.09.2013 and 13.02.2014
Russian version:
Matematicheskii Sbornik, 2014, Volume 205, Number 7, Pages 43–72
DOI: https://doi.org/10.4213/sm8286
Bibliographic databases:
Document Type: Article
UDC: 517.956.8+517.956.227+539.3(3)
MSC: Primary 35Q74; Secondary 74B05
Language: English
Original paper language: Russian
Citation: S. A. Nazarov, “Umov-Mandelshtam radiation conditions in elastic periodic waveguides”, Mat. Sb., 205:7 (2014), 43–72; Sb. Math., 205:7 (2014), 953–982
Citation in format AMSBIB
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    • This publication is cited in the following 34 articles:
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