Abstract
We consider statements of the elasticity problem about the wave propagation in an elastic cylindrical waveguide under different radiation conditions at infinity. For the energy radiation conditions we develop the mathematical theory based on the Mandelstam principle and the Umov–Poynting vector, as well as the technique of weighted spaces with detached asymptotics and the energy flux (symplectic) form. As is shown by examples, the Sommerfeld radiation conditions and the limiting absorption principle contradict the Mandelstam radiation conditions in certain situations. Bibliography: 64 titles. Illustrations: 8 figures.
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