Geodesic
Asymptotics of the solution of Laplace’s equation with third-type boundary conditions on the boundaries of two small holes
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 11, pp. 1768-1783 
S. R. Garifullina; E. Yu. Postnikova. Asymptotics of the solution of Laplace’s equation with third-type boundary conditions on the boundaries of two small holes. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 11, pp. 1768-1783. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_11_a1/
@article{ZVMMF_2013_53_11_a1,
     author = {S. R. Garifullina and E. Yu. Postnikova},
     title = {Asymptotics of the solution of {Laplace{\textquoteright}s} equation with third-type boundary conditions on the boundaries of two small holes},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1768--1783},
     year = {2013},
     volume = {53},
     number = {11},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_11_a1/}
}
TY  - JOUR
AU  - S. R. Garifullina
AU  - E. Yu. Postnikova
TI  - Asymptotics of the solution of Laplace’s equation with third-type boundary conditions on the boundaries of two small holes
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2013
SP  - 1768
EP  - 1783
VL  - 53
IS  - 11
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_11_a1/
LA  - ru
ID  - ZVMMF_2013_53_11_a1
ER  - 
%0 Journal Article
%A S. R. Garifullina
%A E. Yu. Postnikova
%T Asymptotics of the solution of Laplace’s equation with third-type boundary conditions on the boundaries of two small holes
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2013
%P 1768-1783
%V 53
%N 11
%U http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_11_a1/
%G ru
%F ZVMMF_2013_53_11_a1

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

A boundary value problem for Laplace’s equation in a bounded domain with two small holes is considered. Third-type boundary conditions are set on the boundaries of the holes. A Neumann condition is specified on the outer boundary of the domain. A uniform asymptotic approximation of the solution is constructed and justified up to an arbitrary power of a small parameter.

[1] Ilin A. M., Soglasovanie asimptoticheskikh razlozhenii reshenii kraevykh zadach, Nauka, M., 1989 | MR

[2] Ilin A. M., “Kraevaya zadacha dlya ellipticheskogo uravneniya vtorogo poryadka v oblasti s uzkoi schelyu. 2: Oblast s malym otverstiem”, Matem. sb., 103:2 (1977), 265–284 | MR | Zbl

[3] Mazya V. G., Nazarov S. A., Plamenevskii B. A., “Asimptoticheskie razlozheniya sobstvennykh chisel kraevykh zadach dlya operatora Laplasa v oblastyakh s malymi otverstiyami”, Izvestiya AN, ser. matematicheskaya, 48:2 (1984), 347–371 | MR

[4] Maz'ya S., Nazarov S., Plamenevskij B., Asymptotic theory of Elliptic boundary value problems in singularly perturbed domains, Ch. 9, v. 1, Operator Theory, Advances and Applications, 111, Basel-Boston-Berlin, 2000 | MR

[5] Sobolev S. L., Vvedenie v teoriyu kubaturnykh formul, Nauka, M., 1974 | MR

[6] Postnikova E. Yu., “Asimptotika kraevoi zadachi v oblasti s dvumya otverstiyami”, Vestnik Chelyabinskii GU, 2011, no. 26, 49–58

[7] Garifullina S. R., Matematicheskoe modelirovanie i chislennoe issledovanie elektricheskikh polei protyazhennykh elektrodov v poluogranichennom prostranstve, Dis. ... kand. fiz.-matem. nauk, Ufim. gos. aviats.-tekhn. un-t, Ufa, 2011