Uniform exponential dichotomy of parabolic operators with rapidly oscillating coefficients
Matematičeskie zametki, Tome 79 (2006) no. 5, pp. 729-735.

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

The paper deals with averaging problems for parabolic equations. We prove that exponential dichotomy is preserved without any assumption concerning the almost-periodicity of the coefficients.
@article{MZM_2006_79_5_a8,
     author = {V. B. Levenshtam},
     title = {Uniform exponential dichotomy of parabolic operators with rapidly oscillating coefficients},
     journal = {Matemati\v{c}eskie zametki},
     pages = {729--735},
     publisher = {mathdoc},
     volume = {79},
     number = {5},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_5_a8/}
}
TY  - JOUR
AU  - V. B. Levenshtam
TI  - Uniform exponential dichotomy of parabolic operators with rapidly oscillating coefficients
JO  - Matematičeskie zametki
PY  - 2006
SP  - 729
EP  - 735
VL  - 79
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2006_79_5_a8/
LA  - ru
ID  - MZM_2006_79_5_a8
ER  - 
%0 Journal Article
%A V. B. Levenshtam
%T Uniform exponential dichotomy of parabolic operators with rapidly oscillating coefficients
%J Matematičeskie zametki
%D 2006
%P 729-735
%V 79
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2006_79_5_a8/
%G ru
%F MZM_2006_79_5_a8
V. B. Levenshtam. Uniform exponential dichotomy of parabolic operators with rapidly oscillating coefficients. Matematičeskie zametki, Tome 79 (2006) no. 5, pp. 729-735. http://geodesic.mathdoc.fr/item/MZM_2006_79_5_a8/

[1] Zhikov V. V., “Printsip usredneniya dlya parabolicheskikh uravnenii s peremennoi glavnoi chastyu”, Dokl. AN SSSR, 208:1 (1973), 32–35

[2] Zhikov V. V., “Nekotorye voprosy dopustimosti i dikhotomii. Printsip usredneniya”, Izv. AN SSSR. Ser. matem., 40 (1976), 1380–1408 | Zbl

[3] Levitan B. M., Zhikov V. V., Pochti-periodicheskie funktsii i differentsialnye uravneniya, Izd-vo MGU, M., 1978 | Zbl

[4] Levenshtam V. B., “Usrednenie kvazilineinykh parabolicheskikh uravnenii s bystro ostsilliruyuschei glavnoi chastyu. Eksponentsialnaya dikhotomiya”, Izv. RAN. Ser. matem., 56:4 (1992), 813–851 | MR | Zbl

[5] Levenshtam V. B., “Ob odnoznachnoi razreshimosti parabolicheskikh uravnenii s pochti periodicheskimi koeffitsientami v prostranstvakh Geldera”, Matem. zametki, 73:6 (2003), 861–877 | MR | Zbl

[6] Eidelman S. D., Parabolicheskie sistemy, Nauka, M., 1964

[7] Rudin U., Funktsionalnyi analiz, Mir, M., 1975 | MR