Geodesic
Solutions to a singularly perturbed parabolic equation with internal and boundary layers depending on stretched variables of different orders
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 3, pp. 424-437 
E. E. Bukzhalev; A. B. Vasil'eva. Solutions to a singularly perturbed parabolic equation with internal and boundary layers depending on stretched variables of different orders. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 3, pp. 424-437. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_3_a5/
@article{ZVMMF_2007_47_3_a5,
     author = {E. E. Bukzhalev and A. B. Vasil'eva},
     title = {Solutions to a~singularly perturbed parabolic equation with internal and boundary layers depending on stretched variables of different orders},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {424--437},
     year = {2007},
     volume = {47},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_3_a5/}
}
TY  - JOUR
AU  - E. E. Bukzhalev
AU  - A. B. Vasil'eva
TI  - Solutions to a singularly perturbed parabolic equation with internal and boundary layers depending on stretched variables of different orders
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2007
SP  - 424
EP  - 437
VL  - 47
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_3_a5/
LA  - ru
ID  - ZVMMF_2007_47_3_a5
ER  - 
%0 Journal Article
%A E. E. Bukzhalev
%A A. B. Vasil'eva
%T Solutions to a singularly perturbed parabolic equation with internal and boundary layers depending on stretched variables of different orders
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2007
%P 424-437
%V 47
%N 3
%U http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_3_a5/
%G ru
%F ZVMMF_2007_47_3_a5

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

The solution to a singularly perturbed parabolic equation with internal and boundary layers whose stretched variables may depend on different powers of the perturbation parameter is considered. An asymptotic representation of the solution is constructed and substantiated, and its stability is proved.

[1] Bukzhalev E. E., “Kontrastnye struktury tipa stupenki, rastyanutye peremennye kotorykh zavisyat ot razlichnykh stepenei parametra vozmuscheniya”, Zh. vychisl. matem. i matem. fiz., 44:4 (2004), 662–675 | MR | Zbl

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

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

[4] Vasileva A. B., Davydova M. A., “Singulyarno vozmuschennoe uravnenie vtorogo poryadka s malymi parametrami pri pervoi i vtoroi proizvodnykh”, Zh. vychisl. matem. i matem. fiz., 39:9 (1999), 1504–1512 | MR

[5] Bukzhalev E. E., “Singulyarno vozmuschennoe uravnenie s pogransloinym resheniem, rastyanutye peremennye kotorogo zavisyat ot razlichnykh stepenei parametra vozmuscheniya”, Zh. vychisl. matem. i matem. fiz., 43:12 (2003), 1775–1785 | MR | Zbl

[6] Amann H., “Periodic solutions of semi-linear parabolic equations”, Nonlinear Analysis, A Collection of Papers in Honor of Erich Rothe, Acad. Press, New York, 1978, 1–29 | MR

[7] Bukzhalev E. E., “O primenenii metoda differentsialnykh neravenstv k uravneniyam parabolicheskogo tipa, pravaya chast kotorykh rastet po prostranstvennomu gradientu bolee chem kvadratichno”, Differents. ur-niya, 41:3 (2005), 356–365 | MR | Zbl

[8] Kolesov Yu. S., “O nekotorykh priznakakh suschestvovaniya ustoichivykh periodicheskikh reshenii u kvazilineinykh parabolicheskikh uravnenii”, Dokl. AN SSSR, 157:6 (1964), 1288–1290 | MR | Zbl

[9] Butuzov V. F., Nedelko I. V., “Ustoichivost kontrastnykh struktur tipa stupenki v dvumernom sluchae”, Dokl. RAN, 366:3 (1999), 295–298 | MR | Zbl

[10] Butuzov V. F., Nedelko I. V., “O globalnoi oblasti vliyaniya reshenii s vnutrennimi sloyami”, Dokl. RAN, 373:2 (2000), 155–156 | MR | Zbl

[11] Butuzov V. F., Nedelko I. V., “O globalnoi oblasti vliyaniya ustoichivykh reshenii s vnutrennimi sloyami v dvumernom sluchae”, Izv. RAN. Ser. matem., 66:1 (2002), 3–42 | MR | Zbl

[12] Vasileva A. B., Omelchenko O. E., “Periodicheskie kontrastnye struktury tipa stupenki dlya singulyarno vozmuschennogo parabolicheskogo uravneniya”, Differents. ur-niya, 36:2 (2000), 198–208 | MR