Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 10, Tome 89 (1979), pp. 261-269
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M. M. Popov. Correctness of the problem of whispering gallery waves in a vicinity of the-points where boundary's curvature vanishes. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 10, Tome 89 (1979), pp. 261-269. http://geodesic.mathdoc.fr/item/ZNSL_1979_89_a18/
@article{ZNSL_1979_89_a18,
author = {M. M. Popov},
title = {Correctness of the problem of whispering gallery waves in a~vicinity of the-points where boundary's curvature vanishes},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {261--269},
year = {1979},
volume = {89},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_89_a18/}
}
TY - JOUR
AU - M. M. Popov
TI - Correctness of the problem of whispering gallery waves in a vicinity of the-points where boundary's curvature vanishes
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1979
SP - 261
EP - 269
VL - 89
UR - http://geodesic.mathdoc.fr/item/ZNSL_1979_89_a18/
LA - ru
ID - ZNSL_1979_89_a18
ER -
%0 Journal Article
%A M. M. Popov
%T Correctness of the problem of whispering gallery waves in a vicinity of the-points where boundary's curvature vanishes
%J Zapiski Nauchnykh Seminarov POMI
%D 1979
%P 261-269
%V 89
%U http://geodesic.mathdoc.fr/item/ZNSL_1979_89_a18/
%G ru
%F ZNSL_1979_89_a18
Two problems of propagation of whispering gallery waves are considered. The first one arises when in some point $s=0$ boundary's curvature $K(s)$ equal zero, but $\frac{dK}{ds}|_{s=0}\ne0$; the second – when $K(0)=\frac{dK}{ds}|_{s=0}=0$, but $\frac{d^2K}{ds^2}|_{s=0}\ne0$ in a point $s=0$. Using technique of the wave operators of the scattering theory it is proved that each problem has one and only one solution.
