Geodesic
Uniform exponential dichotomy of parabolic operators with rapidly oscillating coefficients
Matematičeskie zametki, Tome 79 (2006) no. 5, pp. 729-735 
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/
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     title = {Uniform exponential dichotomy of parabolic operators with rapidly oscillating coefficients},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_5_a8/}
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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.

[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