Geodesic
Averaging of parabolic inclusions
Sbornik. Mathematics, Tome 195 (2004) no. 1, pp. 19-34 Cet article a éte moissonné depuis la source Math-Net.Ru

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A version of Bogolyubov's first theorem is established for infinite-dimensional parabolic inclusions. Sufficient conditions for the asymptotic stability of the trivial solution of a parabolic inclusion with non-stationary homogeneous principal part are stated. 
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}
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V. S. Klimov. Averaging of parabolic inclusions. Sbornik. Mathematics, Tome 195 (2004) no. 1, pp. 19-34. http://geodesic.mathdoc.fr/item/SM_2004_195_1_a1/

[1] Gaevskii G., Grëger K., Zakharias K., Nelineinye operatornye uravneniya i operatornye differentsialnye uravneniya, Mir, M., 1978 | MR

[2] Blagodatskikh V. I., Filippov A. F., “Differentsialnye vklyucheniya i optimalnoe upravlenie”, Trudy MIAN, 169, 1985, 194–252 | MR | Zbl

[3] Gelman B. D., Obukhovskii V. V., “O novykh rezultatakh v teorii mnogoznachnykh otobrazhenii. II: Analiz i prilozheniya”, Itogi nauki i tekhniki. Matem. analiz, 29, 1991, 107–159 | MR | Zbl

[4] Ioffe A. D., Tikhomirov V. M., Teoriya ekstremalnykh zadach, Nauka, M., 1974 | MR | Zbl

[5] Oben Zh. P., Ekland I., Prikladnoi nelineinyi analiz, Mir, M., 1988 | MR

[6] Tolstonogov A. A., Differentsialnye vklyucheniya v banakhovom prostranstve, Nauka, Novosibirsk, 1986 | MR | Zbl

[7] Filippov A. F., Differentsialnye uravneniya s razryvnoi pravoi chastyu, Nauka, M., 1985 | MR

[8] Castaing C., Valadier V., Convex analysis and measurable multifunctions, Lecture Notes in Math., 580, Springer-Verlag, Berlin, 1977 | MR | Zbl

[9] Dubinskii Yu. A., “Nelineinye ellipticheskie i parabolicheskie uravneniya”, Itogi nauki i tekhniki. Sovr. problemy matem., 9, 1976, 5–130 | Zbl

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

[11] Lions Zh.-L., Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972 | MR

[12] Krasnoselskii M. A., Zabreiko P. P., Pustylnik E. I., Sobolevskii P. E., Integralnye operatory v prostranstvakh summiruemykh funktsii, Nauka, M., 1966 | MR

[13] Klimov V. S., “K zadache o periodicheskikh resheniyakh operatornykh differentsialnykh vklyuchenii”, Izv. AN SSSR. Ser. matem., 53:2 (1989), 309–327 | MR | Zbl

[14] Klimov V. S., “Evolyutsionnye parabolicheskie neravenstva s mnogoznachnymi operatorami”, Matem. sb., 184:8 (1993), 37–54 | MR | Zbl

[15] Klimov V. S., “Ob operatore sdviga po traektoriyam parabolicheskikh vklyuchenii”, Differents. uravneniya, 31:10 (1995), 1716–1721 | MR | Zbl

[16] Klimov V. S., “Ogranichennye resheniya differentsialnykh vklyuchenii s odnorodnoi glavnoi chastyu”, Izv. RAN. Ser. matem., 64:4 (2000), 109–130 | MR | Zbl

[17] Bogolyubov N. N., Mitropolskii Yu. A., Asimptoticheskie metody v teorii nelineinykh kolebanii, Nauka, M., 1974 | MR

[18] Mitropolskii Yu. A., Metod usredneniya v nelineinoi mekhanike, Naukova dumka, Kiev, 1971 | MR

[19] Zhikov V. V., Kozlov S. M., Oleinik O. A., Usrednenie differentsialnykh operatorov, Nauka, M., 1993 | MR | Zbl

[20] Klimov V. S., “O differentsialnykh vklyucheniyakh s odnorodnoi glavnoi chastyu”, Differents. uravneniya, 38:10 (2002), 1382–1389 | MR | Zbl

[21] Chetaev N. G., “K voprosu ob obraschenii teoremy Lagranzha”, Sb. nauchn. trudov Kazanskogo aviats. inst., 1934, no. 2, 29–30

[22] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967