Geodesic
Asymptotic splitting of boundary-value problems for the Helmholtz equation in a~strip with ``permeable'' boundaries
Izvestiya. Mathematics , Tome 61 (1997) no. 4, pp. 877-898

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper is devoted to a boundary-value problem in a strip for the Helmholtz equation. This problem is a mathematical model of a hydro-acoustic waveguide with a permeable boundary. The boundary condition involves a translation-invariant operator symbolizing impendance. It is assumed that the coefficient of the Helmholtz equation varies slowly along the strip. Theorems on the unique solubility of the problem are proved, asymptotic formulae (with respect to the slowness parameter) are derived for its solution, and the practical significance of the results is discussed. 
@article{IM2_1997_61_4_a9,
     author = {S. L. Edelstein},
     title = {Asymptotic splitting of boundary-value problems for the {Helmholtz} equation in a~strip with ``permeable'' boundaries},
     journal = {Izvestiya. Mathematics },
     pages = {877--898},
     publisher = {mathdoc},
     volume = {61},
     number = {4},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1997_61_4_a9/}
}
TY  - JOUR
AU  - S. L. Edelstein
TI  - Asymptotic splitting of boundary-value problems for the Helmholtz equation in a~strip with ``permeable'' boundaries
JO  - Izvestiya. Mathematics 
PY  - 1997
SP  - 877
EP  - 898
VL  - 61
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1997_61_4_a9/
LA  - en
ID  - IM2_1997_61_4_a9
ER  - 
%0 Journal Article
%A S. L. Edelstein
%T Asymptotic splitting of boundary-value problems for the Helmholtz equation in a~strip with ``permeable'' boundaries
%J Izvestiya. Mathematics 
%D 1997
%P 877-898
%V 61
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1997_61_4_a9/
%G en
%F IM2_1997_61_4_a9
S. L. Edelstein. Asymptotic splitting of boundary-value problems for the Helmholtz equation in a~strip with ``permeable'' boundaries. Izvestiya. Mathematics , Tome 61 (1997) no. 4, pp. 877-898. http://geodesic.mathdoc.fr/item/IM2_1997_61_4_a9/