Umov-Mandelshtam radiation conditions in elastic periodic waveguides
Sbornik. Mathematics, Tome 205 (2014) no. 7, pp. 953-982
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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.
@article{SM_2014_205_7_a2,
author = {S. A. Nazarov},
title = {Umov-Mandelshtam radiation conditions in elastic periodic waveguides},
journal = {Sbornik. Mathematics},
pages = {953--982},
publisher = {mathdoc},
volume = {205},
number = {7},
year = {2014},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2014_205_7_a2/}
}
S. A. Nazarov. Umov-Mandelshtam radiation conditions in elastic periodic waveguides. Sbornik. Mathematics, Tome 205 (2014) no. 7, pp. 953-982. http://geodesic.mathdoc.fr/item/SM_2014_205_7_a2/