Geodesic
Evolution parabolic inequalities with multivalued operators
Sbornik. Mathematics, Tome 79 (1994) no. 2, pp. 365-380 Cet article a éte moissonné depuis la source Math-Net.Ru

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Conditions are found under which the set of solutions of an evolution parabolic inequality is nonempty, compact, and connected. Included in the study is the Cauchy problem $f\in y'+Ay$, $y(\alpha)=h$ with a multivalued and monotone operator $A\colon Z^*\to Z$, where $Z$ is a nonreflexive $B$-space. Questions connected with well-posedness of the Cauchy problem and convergence of Faedo–Galërkin approximations are investigated. 
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     author = {V. S. Klimov},
     title = {Evolution parabolic inequalities with multivalued operators},
     journal = {Sbornik. Mathematics},
     pages = {365--380},
     year = {1994},
     volume = {79},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1994_79_2_a7/}
}
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V. S. Klimov. Evolution parabolic inequalities with multivalued operators. Sbornik. Mathematics, Tome 79 (1994) no. 2, pp. 365-380. http://geodesic.mathdoc.fr/item/SM_1994_79_2_a7/

[1] Krasnoselskii M. A., Zabreiko P. P., Geometricheskie metody nelineinogo analiza, Nauka, M., 1975 | MR

[2] Borisovich Yu. G., Gelman B. D., Myshkis A. D., Obukhovskii V. V., “Topologicheskie metody v teorii nepodvizhnykh tochek mnogoznachnykh otobrazhenii”, UMN, 35:1 (1980), 59–126 | MR | Zbl

[3] Borisovich Yu. G., Gelman B. D., Myshkis A. D., Obukhovskii V. V., “Mnogoznachnyi analiz i operatornye vklyucheniya”, Itogi nauki i tekhniki. Sovr. probl. matem. Noveishie dostizheniya, 29, VINITI, M., 1986, 151–211 | MR

[4] Pokhozhaev S. I., “O razreshimosti nelineinykh uravnenii s nechetnymi operatorami”, Funkts. analiz i ego prilozh., 1:3 (1967), 66–73 | MR | Zbl

[5] Bro-w-der F. E., “Pseudo-monotone operators and the direct method of variation”, Arch. Ration Mech. and Anal., 38:4 (1970), 268–277 | DOI | MR

[6] Skrypnik I. V., Metody issledovaniya nelineinykh ellipticheskikh granichnykh zadach, Nauka, M., 1990 | MR

[7] Dubinskii Yu. A., “Nelineinye parabolicheskie uravneniya vysokogo poryadka”, Itogi nauki i tekhniki. Sovr. probl. matem. Noveishie dostizheniya, 37, VINITI, M., 1990, 89–166 | MR

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

[9] Brezis H., “Problemes unilateraux”, J. Math. Pures Appl., 51 (1972), 1–168 | MR | Zbl

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

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

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

[13] Danford N., Shvarts Dzh., Lineinye operatory, 1, Il, M., 1962

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

[15] Mosolov P. P., Myasnikov V. P., Mekhanika zhestkoplasticheskikh sred, Nauka, M., 1981 | MR | Zbl

[16] Senchakova N. V., Tselochislennye kharakteristiki mnogoznachnykh otobrazhenii monotonnogo tipa i operatornye vklyucheniya, Diss. ...kand. fiz.-matem. nauk, BGU, Minsk, 1992

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

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

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

[20] Pankov A. A., Ogranichennye i pochti periodicheskie resheniya nelineinykh differentsialnykh operatornykh uravnenii, Naukova dumka, Kiev, 1985 | MR