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Zapiski Nauchnykh Seminarov LOMI, 1976, Volume 62, Pages 3–20
(Mi znsl2031)
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A point source of oscillations on the boundary of a region
V. M. Babich
Abstract:
The problem of a point source of oscillations on a curve $S$ with curvature which is nowhere zero is considered:
$$
w_{tt}-w_{xx}-w_{yy}=0;\quad w|_{t<0}=0;\quad w|_s=\delta(s-s_0);\quad s,s_0\in S.
$$
The case where the whispering gallery effect arises is investigated: rays issuing from a source $s_0\in S$ and reflected many times from $S$ create this effect. A function containing all singularities of $w$ is constructed explicitly. The theorem that the set of singularities of the function $w$ coincides with the wave fronts of geometrical optics is a consequence of these considerations.
Citation:
V. M. Babich, “A point source of oscillations on the boundary of a region”, Mathematical problems in the theory of wave propagation. Part 8, Zap. Nauchn. Sem. LOMI, 62, "Nauka", Leningrad. Otdel., Leningrad, 1976, 3–20; J. Soviet Math., 11:5 (1979), 665–676
Linking options:
https://www.mathnet.ru/eng/znsl2031 https://www.mathnet.ru/eng/znsl/v62/p3
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Abstract page: | 225 | Full-text PDF : | 106 |
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