TY - JOUR

T1 - Umov-Mandelshtam radiation conditions in elastic periodic waveguides

AU - Nazarov, S.A.

PY - 2014

Y1 - 2014

N2 - © 2014 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd. 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.

AB - © 2014 Russian Academy of Sciences (DoM), London Mathematical Society, Turpion Ltd. 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.

U2 - 10.1070/SM2014v205n07ABEH004405

DO - 10.1070/SM2014v205n07ABEH004405

M3 - Article

VL - 205

SP - 953

EP - 982

JO - Sbornik Mathematics

JF - Sbornik Mathematics

SN - 1064-5616

IS - 7

ER -