Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 13 (2007) no. 2, pp. 124-134
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O. O. Kovrizhnykh. On an asymptotic solution of a singularly perturbed system with two small parameters. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 13 (2007) no. 2, pp. 124-134. http://geodesic.mathdoc.fr/item/TIMM_2007_13_2_a11/
@article{TIMM_2007_13_2_a11,
author = {O. O. Kovrizhnykh},
title = {On an asymptotic solution of a~singularly perturbed system with two small parameters},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {124--134},
year = {2007},
volume = {13},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2007_13_2_a11/}
}
TY - JOUR
AU - O. O. Kovrizhnykh
TI - On an asymptotic solution of a singularly perturbed system with two small parameters
JO - Trudy Instituta matematiki i mehaniki
PY - 2007
SP - 124
EP - 134
VL - 13
IS - 2
UR - http://geodesic.mathdoc.fr/item/TIMM_2007_13_2_a11/
LA - ru
ID - TIMM_2007_13_2_a11
ER -
%0 Journal Article
%A O. O. Kovrizhnykh
%T On an asymptotic solution of a singularly perturbed system with two small parameters
%J Trudy Instituta matematiki i mehaniki
%D 2007
%P 124-134
%V 13
%N 2
%U http://geodesic.mathdoc.fr/item/TIMM_2007_13_2_a11/
%G ru
%F TIMM_2007_13_2_a11
An initial value problem for a singularly perturbed system of two nonlinear ordinary differential equations with two small parameters is considered. An asymptotic expansion of a solution of this problem is constructed under the assumption that the parameters tend to zero independently of each other.
[1] Tikhonov A. N., “Sistemy differentsialnykh uravnenii, soderzhaschie malye parametry pri proizvodnykh”, Mat. sb., 31(73):3 (1952), 575–586 | Zbl
[2] Vasileva A. B., “Asimptoticheskie formuly dlya reshenii sistem obyknovennykh differentsialnykh uravnenii, soderzhaschikh pri proizvodnykh parametry razlichnykh poryadkov malosti”, Dokl. AN SSSR, 128:6 (1959), 1110–1113 | MR
[3] Vasileva A. B., “Asimptoticheskie metody v teorii obyknovennykh differentsialnykh uravnenii s malymi parametrami pri starshikh proizvodnykh”, Zhurn. vychisl. matematiki i mat. fiziki, 3:4 (1963), 611–642 | MR
[4] Ilin A. M., Kovrizhnykh O. O., “Asimptotika resheniya sistemy lineinykh uravnenii s dvumya malymi parametrami”, Dokl. RAN, 396:1 (2004), 23–24 | MR