Geodesic
The asymptotic decomposition of solution of singularly perturbed differential and operational nonlinear equation with variable coefficients
Matematičeskoe modelirovanie, Tome 28 (2016) no. 1, pp. 117-131.

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

Formal asymptotic decomposition on small parameter of solution for initial task for singularly perturbed differential and operator nonlinear equation with variable coefficients in critical case is constructed. Estimates of functions of splash and boundary functions are found, assessment of residual member of decomposition is received.
Keywords: asymptotic decomposition of solution, small parameter, singularly perturbations, differential and operator equations, initial task, critical case, modified method of boundary functions. 
@article{MM_2016_28_1_a8,
     author = {A. V. Zaborskiy and A. V. Nesterov},
     title = {The asymptotic decomposition of solution of singularly perturbed differential and operational nonlinear equation with variable coefficients},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {117--131},
     publisher = {mathdoc},
     volume = {28},
     number = {1},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2016_28_1_a8/}
}
TY  - JOUR
AU  - A. V. Zaborskiy
AU  - A. V. Nesterov
TI  - The asymptotic decomposition of solution of singularly perturbed differential and operational nonlinear equation with variable coefficients
JO  - Matematičeskoe modelirovanie
PY  - 2016
SP  - 117
EP  - 131
VL  - 28
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2016_28_1_a8/
LA  - ru
ID  - MM_2016_28_1_a8
ER  - 
%0 Journal Article
%A A. V. Zaborskiy
%A A. V. Nesterov
%T The asymptotic decomposition of solution of singularly perturbed differential and operational nonlinear equation with variable coefficients
%J Matematičeskoe modelirovanie
%D 2016
%P 117-131
%V 28
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2016_28_1_a8/
%G ru
%F MM_2016_28_1_a8
A. V. Zaborskiy; A. V. Nesterov. The asymptotic decomposition of solution of singularly perturbed differential and operational nonlinear equation with variable coefficients. Matematičeskoe modelirovanie, Tome 28 (2016) no. 1, pp. 117-131. http://geodesic.mathdoc.fr/item/MM_2016_28_1_a8/

[1] A. V. Zaborskii, A. V. Nesterov, “Asimptoticheskoe razlozhenie resheniia singuliarno vozmushchennogo differentsialno-operatornogo uravneniia v kriticheskom sluchae”, Matematicheskoe modelirovanie, 26:4 (2014), 65–79 | Zbl

[2] A. B. Vasileva, V. F. Butuzov, Singuliarno vozmushchennye uravneniia v kriticheskikh sluchaiakh, Izd-vo Mosk. Un-ta, M., 1978, 106 pp. | MR

[3] V. A. Tupchiev, A. N. Chepurko, “Asimptotika resheniia spektralnoi zadachi perenosa neitronov v sloe”, Differentsialnye uravneniia, 32:6 (1996), 847–850

[4] V. N. Latyshev, Ob asimptotike resheniia singuliarno-vozmushchennoi spektralnoi zadachi, voznikaiushchei v teorii perenosa, OIAtE, Obninsk, 1987, 26 pp.

[5] Iu. L. Daletskii, M. G. Krein, Ustoichivost reshenii differentsialnykh uravnenii v banakhovom prostranstve, Nauka, M., 1970, 536 pp. | MR