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Zapiski Nauchnykh Seminarov LOMI, 1976, Volume 62, Pages 3–20 (Mi znsl2031)  

A point source of oscillations on the boundary of a region

V. M. Babich
Full-text PDF (868 kB) Citations (1)
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.
English version:
Journal of Soviet Mathematics, 1979, Volume 11, Issue 5, Pages 665–676
DOI: https://doi.org/10.1007/BF01455043
Bibliographic databases:
UDC: 534.213
Language: Russian
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
Citation in format AMSBIB
\Bibitem{Bab76}
\by V.~M.~Babich
\paper A point source of oscillations on the boundary of a region
\inbook Mathematical problems in the theory of wave propagation. Part~8
\serial Zap. Nauchn. Sem. LOMI
\yr 1976
\vol 62
\pages 3--20
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl2031}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=481555}
\zmath{https://zbmath.org/?q=an:0401.76065|0362.76136}
\transl
\jour J. Soviet Math.
\yr 1979
\vol 11
\issue 5
\pages 665--676
\crossref{https://doi.org/10.1007/BF01455043}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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