Geodesic
On the holomorphic regularization of singularly perturbed systems of differential equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 4, pp. 654-661 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A method for constructing pseudo-holomorphic solutions to strongly nonlinear singularly perturbed systems of differential equations, which a logical continuation of the Lomov regularization method, is proposed. The existence of integrals of such systems, holomorphic in the small parameter, is proven, and sufficient conditions for the convergence of expansion of solutions to these systems in powers of the small parameter in the usual sense are obtained. 
@article{ZVMMF_2017_57_4_a6,
     author = {V. I. Kachalov},
     title = {On the holomorphic regularization of singularly perturbed systems of differential equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {654--661},
     year = {2017},
     volume = {57},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_4_a6/}
}
TY  - JOUR
AU  - V. I. Kachalov
TI  - On the holomorphic regularization of singularly perturbed systems of differential equations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2017
SP  - 654
EP  - 661
VL  - 57
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_4_a6/
LA  - ru
ID  - ZVMMF_2017_57_4_a6
ER  - 
%0 Journal Article
%A V. I. Kachalov
%T On the holomorphic regularization of singularly perturbed systems of differential equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2017
%P 654-661
%V 57
%N 4
%U http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_4_a6/
%G ru
%F ZVMMF_2017_57_4_a6
V. I. Kachalov. On the holomorphic regularization of singularly perturbed systems of differential equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 4, pp. 654-661. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_4_a6/

[1] Vasileva A. B., Butuzov V. F., Asimptoticheskie metody v teorii singulyarnykh vozmuschenii, Vyssh. shkola, M., 1990

[2] Butuzov V. F., Vasileva A. B., Nefedov N. N., “Kontrastnye struktury v singulyarno vozmuschennykh zadachakh”, Fundamentalnaya i prikl. matem., 4:3 (1998), 799–851 | Zbl

[3] Mitropolskii Yu. A., Metod usredneniya v nelineinoi mekhanike, Naukova dumka, Kiev, 1971

[4] Maslov V. P., Asimptoticheskie metody i teoriya vozmuschenii, Nauka, M., 1988

[5] Lomov S. A., Vvedenie v obschuyu teoriyu singulyarnykh vozmuschenii, Nauka, M., 1981

[6] Lomov S. A., Lomov I. S., Osnovy matematicheskoi teorii pogranichnogo sloya, Izd-vo Mosk. un-ta, M., 2011

[7] Lomov I. S., “Neobkhodimye i dostatochnye usloviya suschestvovaniya tselykh analiticheskikh reshenii singulyarno vozmuschennykh uravnenii”, Dokl. AN SSSR, 299:4 (1988), 811–815 | Zbl

[8] Lomov S. A., “Analiticheskie resheniya singulyarno vozmuschennykh zadach”, Dokl. AN SSSR, 265:3 (1982), 529–533 | Zbl

[9] Kachalov V. I., Lomov S. A., “Gladkost reshenii differentsialnykh uravnenii po singulyarno vkhodyaschemu parametru”, Dokl. AN SSSR, 299:4 (1988), 805–808 | Zbl

[10] Kachalov V. I., Lomov S. A., “Psevdoanaliticheskie resheniya singulyarno vozmuschennykh zadach”, Dokl. RAN, 334:6 (1994), 694–695 | Zbl

[11] Radyno Ya. V., “Prostranstvo vektorov eksponentsialnogo tipa”, Dokl. AN BSSR, 27:9 (1983), 791–793 | Zbl

[12] Babikov Yu. N., Obschii kurs obyknovennykh differentsialnykh uravnenii, Izd-vo Leningr. un-ta, L., 1981

[13] Samoilenko A. M., Krivosheya S. A., Perestyuk N. A., Differentsialnye uravneniya, Vysshaya shkola, M., 1989

[14] Kachalov V. I., “Golomorfnaya regulyarizatsiya singulyarno vozmuschennykh zadach”, Vestn. MEI, 2010, no. 6, 54–62