Geodesic
The buffer boundary layer in a~mixed boundary value problem with contrasting coefficients
Sibirskij žurnal industrialʹnoj matematiki, Tome 14 (2011) no. 4, pp. 63-75.

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

We construct asymptotics for the solution to a mixed boundary value problem in a thin compound cylinder $\Omega_h^0\cup\Omega_h^1\cup\dots\cup\Omega_h^J$ for a scalar second-order differential equation with piecewise linear coefficients of orders $h^m$ in $\Omega_h^0$ and $h^0$ in $\Omega_h^j$, $j=1,\dots,J$, where $h>0$ is a small parameter, and $m=0,1,2$ (the typical cases). For $m=1$ and $J>1$ we discover the new phenomenon of a one-dimensional buffer boundary layer, which enables us to combine smooth-type expansion to a higher-dimensional boundary layer concentrated in the immediate vicinity of the bases of the cylinder.
Keywords: thin region, contrasting coefficients, asymptotics, buffer boundary layer. 
@article{SJIM_2011_14_4_a6,
     author = {S. A. Nazarov and A. S. Slutskiǐ},
     title = {The buffer boundary layer in a~mixed boundary value problem with contrasting coefficients},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {63--75},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2011_14_4_a6/}
}
TY  - JOUR
AU  - S. A. Nazarov
AU  - A. S. Slutskiǐ
TI  - The buffer boundary layer in a~mixed boundary value problem with contrasting coefficients
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2011
SP  - 63
EP  - 75
VL  - 14
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2011_14_4_a6/
LA  - ru
ID  - SJIM_2011_14_4_a6
ER  - 
%0 Journal Article
%A S. A. Nazarov
%A A. S. Slutskiǐ
%T The buffer boundary layer in a~mixed boundary value problem with contrasting coefficients
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2011
%P 63-75
%V 14
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2011_14_4_a6/
%G ru
%F SJIM_2011_14_4_a6
S. A. Nazarov; A. S. Slutskiǐ. The buffer boundary layer in a~mixed boundary value problem with contrasting coefficients. Sibirskij žurnal industrialʹnoj matematiki, Tome 14 (2011) no. 4, pp. 63-75. http://geodesic.mathdoc.fr/item/SJIM_2011_14_4_a6/

[1] Nazarov S. A., Asimptoticheskaya teoriya tonkikh plastin i sterzhnei. Ponizhenie razmernosti i integralnye otsenki, Nauch. kniga, Novosibirsk, 2001

[2] Vishik M. I., Lyusternik L. A., “Regulyarnoe vyrozhdenie i pogranichnyi sloi dlya lineinykh differentsialnykh uravnenii s malym parametrom”, Uspekhi mat. nauk, 12:5 (1957), 3–122 | MR | Zbl

[3] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973 | MR