This article is cited in 18 scientific papers (total in 18 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
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.
elastic periodic waveguide, Mandelshtam's energy radiation condition, Umov-Poynting vector, energy transfer symplectic form.
PDF file (818 kB)
Sbornik: Mathematics, 2014, 205:7, 953–982
MSC: Primary 35Q74; Secondary 74B05
Received: 26.09.2013 and 13.02.2014
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
\paper Umov-Mandelshtam radiation conditions in elastic periodic waveguides
\jour Mat. Sb.
\jour Sb. Math.
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