Geodesic
Asymptotic integration of the linear parabolic problem with the high frequency coefficients in the critical case
Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 4, pp. 19-23 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A concrete (illustrative) example of the linear parabolic problem with two independent variables and high-frequency coefficients in time is considered. The corresponding stationary homogeneous averaged problem is degenerate. Using the method developed recently for an ordinary differential equations [1] and the method of boundary layer a full formal asymptotics of the periodic solution in time is constructed. 
@article{VMJ_2012_14_4_a2,
     author = {V. V. Gusachenko and V. B. Levenshtam},
     title = {Asymptotic integration of the linear parabolic problem with the high frequency coefficients in the critical case},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {19--23},
     year = {2012},
     volume = {14},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2012_14_4_a2/}
}
TY  - JOUR
AU  - V. V. Gusachenko
AU  - V. B. Levenshtam
TI  - Asymptotic integration of the linear parabolic problem with the high frequency coefficients in the critical case
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2012
SP  - 19
EP  - 23
VL  - 14
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VMJ_2012_14_4_a2/
LA  - ru
ID  - VMJ_2012_14_4_a2
ER  - 
%0 Journal Article
%A V. V. Gusachenko
%A V. B. Levenshtam
%T Asymptotic integration of the linear parabolic problem with the high frequency coefficients in the critical case
%J Vladikavkazskij matematičeskij žurnal
%D 2012
%P 19-23
%V 14
%N 4
%U http://geodesic.mathdoc.fr/item/VMJ_2012_14_4_a2/
%G ru
%F VMJ_2012_14_4_a2
V. V. Gusachenko; V. B. Levenshtam. Asymptotic integration of the linear parabolic problem with the high frequency coefficients in the critical case. Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 4, pp. 19-23. http://geodesic.mathdoc.fr/item/VMJ_2012_14_4_a2/

[1] Do N. T., Levenshtam V. B., “Asimptoticheskoe integrirovanie sistemy differentsialnykh uravnenii s vysokochastotnymi slagaemymi v kriticheskom sluchae”, Differents. uravneniya, 48:8 (2012), 1190–1192 | MR | Zbl

[2] Do N. T., Levenshtam V. B., “Asimptoticheskoe integrirovanie sistemy differentsialnykh uravnenii s bolshim parametrom v kriticheskom sluchae”, Zhurn. vychislitelnoi matematiki i mat. fiziki, 51:6 (2011), 1043–1055 | MR | Zbl

[3] Vishik M. I., Lyusternik L. A., “Reshenie nekotorykh zadach v sluchae matrits i samosopryazhennykh i nesamosopryazhennykh differentsialnykh uravnenii”, Uspekhi mat. nauk, 15:3 (1960), 3–80 | MR | Zbl

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