Geodesic
On the asymptotic behavior of the solution of a singularly perturbed system of parabolic equations in the critical case
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 2, pp. 268-275 
A. V. Nesterov; O. V. Shuliko. On the asymptotic behavior of the solution of a singularly perturbed system of parabolic equations in the critical case. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 2, pp. 268-275. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_2_a6/
@article{ZVMMF_2010_50_2_a6,
     author = {A. V. Nesterov and O. V. Shuliko},
     title = {On the asymptotic behavior of the solution of a singularly perturbed system of parabolic equations in the critical case},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {268--275},
     year = {2010},
     volume = {50},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_2_a6/}
}
TY  - JOUR
AU  - A. V. Nesterov
AU  - O. V. Shuliko
TI  - On the asymptotic behavior of the solution of a singularly perturbed system of parabolic equations in the critical case
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2010
SP  - 268
EP  - 275
VL  - 50
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_2_a6/
LA  - ru
ID  - ZVMMF_2010_50_2_a6
ER  - 
%0 Journal Article
%A A. V. Nesterov
%A O. V. Shuliko
%T On the asymptotic behavior of the solution of a singularly perturbed system of parabolic equations in the critical case
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2010
%P 268-275
%V 50
%N 2
%U http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_2_a6/
%G ru
%F ZVMMF_2010_50_2_a6

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

A formal asymptotic representation is constructed for the solution of an initial-boundary value problem for a singularly perturbed system of parabolic equations. A specific feature of the problem is that its solution has an internal transition layer.

[1] Nesterov A. V., “Ob asimptotike resheniya sistemy uravnenii diffuziya–sorbtsiya pri malykh koeffitsientakh diffuzii”, Zh. vychisl. matem. i matem. fiz., 29:9 (1989), 1318–1330 | MR

[2] Nesterov A. V., “O vnutrennikh perekhodnykh parabolicheskikh sloyakh”, Matem. idei P. L. Chebysheva i ikh prilozh. k sovrem. probl. estestvoznaniya, Tezisy dokl. Mezhdunar. konf., IATE, Obninsk, 2002

[3] Nesterov A. V., Shuliko O. V., “Asimptotika resheniya singulyarno vozmuschennoi sistemy differentsialnykh uravnenii pervogo poryadka v chastnykh proizvodnykh v kriticheskom sluchae”, Matem. idei P. L. Chebysheva i ikh prilozh. k sovrem. probl. estestvoznaniya, Tezisy dokl. konf., Obninsk, 2004

[4] Nesterov A. V., Shuliko O. V., “Asimptotika resheniya slabo nelineinoi sistemy differentsialnykh uravnenii tipa “reaktsiya–diffuziya””, Matem. modelirovanie, 16:8 (2004), 50–58 | MR | Zbl

[5] Nesterov A. V., Shuliko O. V., “The asymptotic solution of singularly perturbed system of first order partial differential equation in critical case”, Math. Modeling and Analysis, Tezisy dokl. konf., Trakai, 2005

[6] Nesterov A. V., Shuliko O. V., “Asimptotika resheniya singulyarno vozmuschennoi sistemy differentsialnykh uravnenii pervogo poryadka v chastnykh proizvodnykh s maloi nelineinostyu v kriticheskom sluchae”, Zh. vychisl. matem. i matem. fiz., 47:3 (2007), 438–444 | MR | Zbl

[7] Vasileva A. B., Butuzov V. F., Singulyarno vozmuschennye uravneniya v kriticheskikh sluchayakh, Izd-vo MGU, M., 1978 | MR