Geodesic
On the asymptotics of the Goursat problem with a power boundary layer
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 224 (2023), pp. 65-70.

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

In this paper, we consider the Goursat problem for a partial differential equation containing a small parameter $\varepsilon$ in the coefficient of the highest derivative. For $\varepsilon=0$, the order of the equation does not decrease, but a singularity appears, which has the nature of a power boundary layer. A solution of the singularly perturbed Gaussian problem is constructed in the form of a formal series in powers of the small parameter. The asymptotic nature of the constructed series is proved.
Keywords: singularly perturbed differential equation, asymptotic integration, power boundary layer
Mots-clés : Goursat problem. 
@article{INTO_2023_224_a7,
     author = {I. V. Zakharova},
     title = {On the asymptotics of the {Goursat} problem with a power boundary layer},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {65--70},
     publisher = {mathdoc},
     volume = {224},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_224_a7/}
}
TY  - JOUR
AU  - I. V. Zakharova
TI  - On the asymptotics of the Goursat problem with a power boundary layer
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2023
SP  - 65
EP  - 70
VL  - 224
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2023_224_a7/
LA  - ru
ID  - INTO_2023_224_a7
ER  - 
%0 Journal Article
%A I. V. Zakharova
%T On the asymptotics of the Goursat problem with a power boundary layer
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2023
%P 65-70
%V 224
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2023_224_a7/
%G ru
%F INTO_2023_224_a7
I. V. Zakharova. On the asymptotics of the Goursat problem with a power boundary layer. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Optimal Control, Tome 224 (2023), pp. 65-70. http://geodesic.mathdoc.fr/item/INTO_2023_224_a7/

[1] Zakharova I. V., “Postroenie asimptoticheskikh reshenii nekotorykh vyrozhdayuschikhsya differentsialnykh uravnenii s malym parametrom”, Itogi nauki tekhn. Sovr. mat. prilozh. Temat. obzory., 212 (2022), 50–56 | DOI

[2] Lomov S. A., Lomov I. S., Osnovy matematicheskoi teorii pogranichnogo sloya, Izd-vo MGU, M., 2011

[3] Lomov S. A., “Stepennoi pogranichnyi sloi v zadachakh s singulyarnym vozmuscheniem”, Izv. AN SSSR. Ser. mat., 30:3 (1966), 525–572 | Zbl

[4] Lomov S. A., “Stepennoi pogranichnyi sloi v zadachakh s malym parametrom”, Dokl. AN SSSR., 148:3 (1963), 516–519 | Zbl

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