Geodesic
Time asymptotics of a field excited in a waveguide by a harmonic current
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 12, pp. 2219-2231

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A three-dimensional regular waveguide is examined. The limiting amplitude principle for frequencies other than the cutoff frequencies is substantiated. The asymptotic behavior of the solution to the problem of excitation of oscillations by a current of the form $fe^{-i\omega t}$ at large $t$ is found both for frequencies other than the cutoff frequencies and for a frequency coinciding with one of the cutoff frequencies (in the case of the resonance). 
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     author = {A. N. Bogolyubov and M. D. Malykh and A. A. Panin},
     title = {Time asymptotics of a field excited in a waveguide by a harmonic current},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2219--2231},
     publisher = {mathdoc},
     volume = {45},
     number = {12},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_12_a10/}
}
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A. N. Bogolyubov; M. D. Malykh; A. A. Panin. Time asymptotics of a field excited in a waveguide by a harmonic current. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 12, pp. 2219-2231. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_12_a10/