Geodesic
Averaging of quasilinear parabolic equations with rapidly oscillating principal part. Exponential dichotomy
Izvestiya. Mathematics, Tome 41 (1993) no. 1, pp. 95-132 
V. B. Levenshtam. Averaging of quasilinear parabolic equations with rapidly oscillating principal part. Exponential dichotomy. Izvestiya. Mathematics, Tome 41 (1993) no. 1, pp. 95-132. http://geodesic.mathdoc.fr/item/IM2_1993_41_1_a4/
@article{IM2_1993_41_1_a4,
     author = {V. B. Levenshtam},
     title = {Averaging of quasilinear parabolic equations with rapidly oscillating principal part. {Exponential} dichotomy},
     journal = {Izvestiya. Mathematics},
     pages = {95--132},
     year = {1993},
     volume = {41},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1993_41_1_a4/}
}
TY  - JOUR
AU  - V. B. Levenshtam
TI  - Averaging of quasilinear parabolic equations with rapidly oscillating principal part. Exponential dichotomy
JO  - Izvestiya. Mathematics
PY  - 1993
SP  - 95
EP  - 132
VL  - 41
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/IM2_1993_41_1_a4/
LA  - en
ID  - IM2_1993_41_1_a4
ER  - 
%0 Journal Article
%A V. B. Levenshtam
%T Averaging of quasilinear parabolic equations with rapidly oscillating principal part. Exponential dichotomy
%J Izvestiya. Mathematics
%D 1993
%P 95-132
%V 41
%N 1
%U http://geodesic.mathdoc.fr/item/IM2_1993_41_1_a4/
%G en
%F IM2_1993_41_1_a4

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

The first part of this article is an investigation of the question of preservation of an exponential dichotomy for solutions of a linear parabolic equation upon a high-frequency perturbation of its principal terms. The second part contains a justification of the averaging principle on the whole time axis for quasilinear parabolic equations with rapidly oscillating principal part.

[1] Zhikov V. V., “Nekotorye voprosy dopustimosti i dikhotomii. Printsip usredneniya”, Izv. AN SSSR. Ser. matem., 40:6 (1976), 1380–1408 | MR | Zbl

[2] Kolesov Yu. S., “Ob ustoichivosti reshenii lineinykh differentsialnykh uravnenii parabolicheskogo tipa s pochti periodicheskimi koeffitsientami”, Tr. MMO, 1978, 3–27 | MR | Zbl

[3] Eidelman S. D., Parabolicheskie sistemy, Nauka, M., 1964, 443 pp. | MR

[4] Daletskii Yu. L., Krein M. G., Ustoichivost reshenii differentsialnykh uravnenii v banakhovom prostranstve, Nauka, M., 1970 | MR

[5] Levenshtam V V., Printsip usredneniya v sluchae zadachi Koshi dlya kvazilineinykh parabolicheskikh uravnenii, Dep. v VINITI 2.11.87, No 7672-V87

[6] Mikhlin S. G., Lineinye uravneniya v chastnykh proizvodnykh, Vyssh. shk., M., 1977, 431 pp. | MR

[7] Mukhamadiev E., “Ob obratimosti differentsialnykh operatorov v chastnykh proizvodnykh ellipticheskogo tipa”, DAN SSSR, 205:6 (1972), 1292–1295 | Zbl

[8] Shubin M. A., “Pochti periodicheskie funktsii i differentsialnye operatory s chastnymi proizvodnymi”, UMN, 33:2(200) (1978), 3–47 | MR | Zbl

[9] Simonenko I. B., “Obosnovanie metoda usredneniya dlya abstraktnykh parabolicheskikh uravnenii”, Matem. sb., 81(123):1 (1970), 53–61 | MR | Zbl

[10] Simonenko I. V., Metod usredneniya v teorii nelineinykh uravnenii parabolicheskogo tipa s prilozheniem k zadacham gidrodinamicheskoi ustoichivosti, Rostovsk. univer., Rostov-na Donu, 1989, 112 pp. | Zbl