Geodesic
The boundary problem for elliptic equation with conductivity coefficient in three-dimentional case
Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 14 (2011), pp. 85-93 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The boundary problem for elliptic equation in a three-dimensional cylindrical region, divided into sectors with corner angle being a small parameter is considered. Thermal conductivity coefficient of composite material is rapidly oscillating function. The period of this coefficient is equal to $\varepsilon$. This problem is a generalization previously considered two-dimensional, for the solution of which an asymptotic expansion in powers of small parameter was built with method two-scale expansions. Moreover, it is succeed to avoid problems associated with corner points in three dimensions because of the appearance of region under consideration.
Keywords: boundary problem, asymptotic expansion
Mots-clés : elliptic equation. 
@article{VCHGU_2011_14_a7,
     author = {I. S. Malakhova},
     title = {The boundary problem for elliptic equation with conductivity coefficient in three-dimentional case},
     journal = {Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika},
     pages = {85--93},
     year = {2011},
     number = {14},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VCHGU_2011_14_a7/}
}
TY  - JOUR
AU  - I. S. Malakhova
TI  - The boundary problem for elliptic equation with conductivity coefficient in three-dimentional case
JO  - Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika
PY  - 2011
SP  - 85
EP  - 93
IS  - 14
UR  - http://geodesic.mathdoc.fr/item/VCHGU_2011_14_a7/
LA  - ru
ID  - VCHGU_2011_14_a7
ER  - 
%0 Journal Article
%A I. S. Malakhova
%T The boundary problem for elliptic equation with conductivity coefficient in three-dimentional case
%J Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika
%D 2011
%P 85-93
%N 14
%U http://geodesic.mathdoc.fr/item/VCHGU_2011_14_a7/
%G ru
%F VCHGU_2011_14_a7
I. S. Malakhova. The boundary problem for elliptic equation with conductivity coefficient in three-dimentional case. Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 14 (2011), pp. 85-93. http://geodesic.mathdoc.fr/item/VCHGU_2011_14_a7/

[1] N. S. Bakhvalov, G. P. Panasenko, Osrednenie protsessov v periodicheskikh sredakh, Nauka, M., 1984

[2] A. M. Ilin, A. R. Danilin, Asimptoticheskie metody v analize, Fizmatlit, M., 2009

[3] I. S. Malakhova, “Kraevaya zadacha dlya ellipticheskogo uravneniya s bystroostsilliruyuschimi koeffitsientami v pryamougolnike”, Zhurn. vychisl. matematiki i mat. fiziki, 51:8 (2011), 1457–1466

[4] S. A. Nazarov, “Asimptotika resheniya zadachi Dirikhle dlya uravneniya s bystroostsilliruyuschimi koeffitsientami v pryamougolnike”, Mat. sb., 182:5 (1991), 692–722