Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 23, Tome 210 (1994), pp. 125-145
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S. A. Kochengin. A problem of a point source of $SH$-waves in a case of separation of the variables. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 23, Tome 210 (1994), pp. 125-145. http://geodesic.mathdoc.fr/item/ZNSL_1994_210_a10/
@article{ZNSL_1994_210_a10,
author = {S. A. Kochengin},
title = {A problem of a~point source of $SH$-waves in a~case of separation of the variables},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {125--145},
year = {1994},
volume = {210},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_210_a10/}
}
TY - JOUR
AU - S. A. Kochengin
TI - A problem of a point source of $SH$-waves in a case of separation of the variables
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1994
SP - 125
EP - 145
VL - 210
UR - http://geodesic.mathdoc.fr/item/ZNSL_1994_210_a10/
LA - ru
ID - ZNSL_1994_210_a10
ER -
%0 Journal Article
%A S. A. Kochengin
%T A problem of a point source of $SH$-waves in a case of separation of the variables
%J Zapiski Nauchnykh Seminarov POMI
%D 1994
%P 125-145
%V 210
%U http://geodesic.mathdoc.fr/item/ZNSL_1994_210_a10/
%G ru
%F ZNSL_1994_210_a10
The equation $$ \operatorname{div}(\mu\nabla u)+\omega^2\rho u=-\delta(x-x_0)\delta(y-y_0), $$ where $\mu(x,y)=a(x)b(y)=a(x)b(y)(c(x)+d(y))$ ($a,b,c,d$ are given step functions) is considered. The problem is solved in explicit form and its asymptotic expansion, if $\omega\to0$, is found. Bibliography: 8 titles.
