Asymptotic expansion of the solution of the bisingularly perturbed elliptic equation
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 6 (2013), pp. 37-44 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Using a generalized method of boundary functions, a uniform asymptotic expansion of the solution of the Dirichlet problem for the bisingularly perturbed second order elliptic equation is constructed.
Keywords: asymptotic expansion, Dirichlet problem, Laplace operator, turning point.
Mots-clés : elliptic equation, bisingular perturbation
@article{VTGU_2013_6_a4,
     author = {D. A. Tursunov},
     title = {Asymptotic expansion of the solution of the bisingularly perturbed elliptic equation},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {37--44},
     year = {2013},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2013_6_a4/}
}
TY  - JOUR
AU  - D. A. Tursunov
TI  - Asymptotic expansion of the solution of the bisingularly perturbed elliptic equation
JO  - Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
PY  - 2013
SP  - 37
EP  - 44
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/VTGU_2013_6_a4/
LA  - ru
ID  - VTGU_2013_6_a4
ER  - 
%0 Journal Article
%A D. A. Tursunov
%T Asymptotic expansion of the solution of the bisingularly perturbed elliptic equation
%J Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
%D 2013
%P 37-44
%N 6
%U http://geodesic.mathdoc.fr/item/VTGU_2013_6_a4/
%G ru
%F VTGU_2013_6_a4
D. A. Tursunov. Asymptotic expansion of the solution of the bisingularly perturbed elliptic equation. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 6 (2013), pp. 37-44. http://geodesic.mathdoc.fr/item/VTGU_2013_6_a4/

[1] Alymkulov K., “Analog metoda pogranfunktsii dlya resheniya modelnogo uravneniya Laitkhilla, v sluchae, kogda nevozmuschennoe uravnenie imeet polyus lyubogo poryadka v regulyarnoi osoboi tochke”, Differentsialnye uravneniya i optimalnoe uparvlenie, Cb. tezisov konf., posvyasch. 90-letiyu so dnya rozhdeniya akademika E. F. Mischenko, M., 2012, 12–14

[2] Alymkulov K., “Extension of boundary layer function method for singularly perturbed differential equation of Prandtle–Tichonov and Lighthill types”, Reports of the Third Congress of the World Mathematical Society of Turkic Countries (Almaty, June–July, 2009), 256–259

[3] Ilin A. M., Danilin A. R., Asimptoticheskie metody v analize, FIZMATLIT, M., 2009, 248 pp.

[4] Ilin A. M., Soglasovanie asimptoticheskikh razlozhenii kraevykh zadach, Nauka, M., 1989, 334 pp. | MR

[5] Vishik M. I., Lyusternik L. A., “Regulyarnoe vyrozhdenie i pogranichnyi sloi dlya lineinykh differentsialnykh uravnenii s malym parametrom”, UMN, 12:5(77) (1957), 3–122 | MR | Zbl

[6] Zaitsev V., Polyanin A. D., Spravochnik po obyknovennym differentsialnym uravneniyam, Nauka, M., 1995, 560 pp. | MR

[7] Gilbarg D., Trudinger N., Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989, 464 pp. | MR | Zbl