Geodesic
Attractors of partial differential evolution equations and estimates of their dimension
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 38 (1983) no. 4, pp. 151-213 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{RM_1983_38_4_a9,
     author = {A. V. Babin and M. I. Vishik},
     title = {Attractors of partial differential evolution equations and estimates of their dimension},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {151--213},
     year = {1983},
     volume = {38},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_1983_38_4_a9/}
}
TY  - JOUR
AU  - A. V. Babin
AU  - M. I. Vishik
TI  - Attractors of partial differential evolution equations and estimates of their dimension
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 1983
SP  - 151
EP  - 213
VL  - 38
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/RM_1983_38_4_a9/
LA  - en
ID  - RM_1983_38_4_a9
ER  - 
%0 Journal Article
%A A. V. Babin
%A M. I. Vishik
%T Attractors of partial differential evolution equations and estimates of their dimension
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 1983
%P 151-213
%V 38
%N 4
%U http://geodesic.mathdoc.fr/item/RM_1983_38_4_a9/
%G en
%F RM_1983_38_4_a9
A. V. Babin; M. I. Vishik. Attractors of partial differential evolution equations and estimates of their dimension. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 38 (1983) no. 4, pp. 151-213. http://geodesic.mathdoc.fr/item/RM_1983_38_4_a9/

[1] V. I. Arnold, Dopolnitelnye glavy teorii obyknovennykh differentsialnykh uravnenii, Nauka, M., 1978 | MR

[2] Z. Nitetski, Vvedenie v differentsialnuyu dinamiku, Mir, M., 1975 | MR | Zbl

[3] Strannye attraktory, sb. statei, Mir, M., 1981 | MR

[4] Dzh. Marsden, M. Mak-Kraken, Bifurkatsiya rozhdeniya tsikla i ee prilozheniya, Mir, M., 1980 | MR

[5] D. Henry, 840, Lect. Notes in Math., Springer-Verlag, Berlin, 1981 | MR

[6] S. Smale, “Differentiable dynamical systems”, Bull. Amer. Math. Soc., 73:6 (1967), 747–817 | DOI | MR

[7] Dzh. Milnor, Teoriya Morsa, Mir, M., 1965 | MR

[8] R. S. Palais, S. Smale, “A generalized Morse theory”, Bull. Amer. Math. Soc., 70:1 (1964), 165–172 | DOI | MR | Zbl

[9] O. A. Ladyzhenskaya, “O dinamicheskoi sisteme, porozhdaemoi uravneniyami Nave–Stoksa”, Zap. nauchn. sem. LOMI, 27 (1972), 91–115 | Zbl

[10] J. Mallet-Paret, “Negatively invariant sets of compact maps and an extension of a theorem of Cartwright”, J. Diff. equations, 22 (1976), 331–348 | DOI | MR | Zbl

[11] C. Foias, R. Temam, “Some analytic and geometric properties of the solutions of the evolution Navier–Stokes equations”, J. Math. Pures Appl., 58:3 (1979), 339–368 | MR | Zbl

[12] Yu. S. Ilyashenko, “Slabo szhimayuschie sistemy i attraktory galerkinskikh priblizhenii uravnenii Nave–Stoksa”, UMN, 36:3 (1981), 243–244

[13] A. V. Babin, M. I. Vishik, “Attraktory sistemy Nave–Stoksa i parabolicheskikh uravnenii i otsenka ikh razmernosti”, Zap. nauchn. sem. LOMI, 115 (1982), 5–15 | MR

[14] O. A. Ladyzhenskaya, “O konechnomernosti ogranichennykh invariantnykh mnozhestv dlya sistemy Nave–Stoksa i drugikh dissipativnykh sistem”, Zap. nauchn. sem. LOMI, 115 (1982), 137–155 | MR | Zbl

[15] D. A. Kamaev, “O gipoteze Khopfa dlya odnogo klassa uravnenii khimicheskoi kinetiki”, Zap. nauchn. sem. LOMI, 110 (1981), 57–73 | MR | Zbl

[16] N. V. Nikolenko, “Invariantnye, asimptoticheski ustoichivye tory vozmuschennogo uravneniya Kortevega–de Friza”, UMN, 35:5 (1980), 121–180 | MR | Zbl

[17] L. D. Meshalkin, Ya. G. Sinai, “Issledovanie ustoichivosti statsionarnogo resheniya odnoi sistemy uravnenii ploskogo dvizheniya neszhimaemoi vyazkoi zhidkosti”, Prikl. matem. i mekh., 25:6 (1961), 1140–1143 | Zbl

[18] V. I. Yudovich, “O neustoichivosti parallelnykh techenii vyazkoi neszhimaemoi zhidkosti otnositelno prostranstvenno-periodicheskikh vozmuschenii”, Chislennye metody resheniya zadach matematicheskoi fiziki, Nauka, M., 1966, 242–249

[19] J. C. Wells, “Invariant manifolds of nonlinear operators”, Pacific. J. of Math., 62:1 (1976), 285–293 | MR | Zbl

[20] S. L. Sobolev, Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, Izd-vo LGU, L., 1950

[21] O. V. Besov, V. P. Ilin, S. M. Nikolskii, Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1975 | MR | Zbl

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

[23] M. I. Vishik, “O razreshimosti kraevykh zadach dlya kvazilineinykh parabolicheskikh uravnenii vysshikh poryadkov”, Matem. sb., 59 (1962), 289–325 | Zbl

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

[25] R. Temam, Uravneniya Nave–Stoksa. Teoriya i chislennyi analiz, Mir, M., 1981 | MR | Zbl

[26] A. V. Babin, M. J. Vishik, “Regular attractors of semigroups and evolution equations”, J. Math. Pures Appl., 1983 | MR

[27] A. V. Babin, “Konechnomernost yadra i koyadra kvazilineinykh ellipticheskikh otobrazhenii”, Matem. sb., 93:3 (1974), 422–450 | MR | Zbl

[28] Dzh. V. S. Kassels, Vvedenie v geometriyu chisel, Mir, M., 1965 | MR

[29] V. Gurevich, G. Volmen, Teoriya razmernosti, IL, M., 1948

[30] Zh.-L. Lions, E. Madzhenes, Neodnorodnye granichnye zadachi i ikh prilozheniya, Mir, M., 1971 | Zbl

[31] I. Ts. Gokhberg, M. G. Krein, Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov, Nauka, M., 1965

[32] O. L. Ladyzhenskaya, Matematicheskie voprosy dinamiki vyazkoi neszhimaemoi zhidkosti, Fizmatgiz, M., 1961

[33] A. I. Volpert, A. N. Ivanova, O prostranstvenno neodnorodnykh resheniyakh nelineinykh diffuzionnykh uravnenii, Preprint in-ta khim. fiziki AN SSSR, Chernogolovka, 1981

[34] A. V. Babin, M. I. Vishik, “Attraktory kvazilineinykh parabolicheskikh uravnenii”, DAN, 254:4 (1982), 780–784 | MR

[35] A. V. Babin, M. I. Vishik, “Suschestvovanie i otsenka razmernosti attraktorov kvazilineinykh parabolicheskikh uravnenii i sistemy Nave–Stoksa”, UMN, 37:3 (1982), 173–174 | MR | Zbl

[36] A. I. Volpert, S. I. Xudyaev, Analiz v klassakh razryvnykh funktsii i uravneniya matematicheskoi fiziki, Nauka, M., 1975 | MR

[37] A. I. Volpert, R. S. Tishakova, Polozhitelnye resheniya kvazilineinykh parabolicheskikh sistem uravnenii, Preprint in-ta khim. fiziki AN SSSR, Chernogolovka, 1980

[38] A. V. Babin, M. I. Vishik, “Regulyarnyi attraktor giperbolicheskogo uravneniya”, UMN, 37:4 (1982), 89–90 | MR

[39] M. Rid, B. Saimon, Metody sovremennoi matematicheskoi fiziki, t. 4, Mir, M., 1982

[40] Yu. S. Ilyashenko, A. N. Chetaev, “O razmernosti attraktorov dlya odnogo klassa dissipativnykh sistem”, Prikl. matem. i mekh., 46:3 (1982), 374–381 | MR

[41] Yu. S. Ilyashenko, “Slabo szhimayuschie sistemy i attraktory galerkinskikh priblizhenii uravnenii Nave–Stoksa na dvumernom tore”, Uspekhi mekhaniki, 1982, no. 1, 31–63 | MR

[42] A. Douady, J. Oesterle, “Dimension de Hausdorff des attracteurs”, C. R. Acad. Sci., 290 (1980), 1135–1138 | MR | Zbl

[43] C. Foias, 0. P. Manley, R. Temam, Y. M. Treve, “Asymptotic analysis of the Navier–Stokes equations”, Prepublications Université de Paris-Sud,, 82T32, 1–51

[44] H. Brezis, T. Gallouet, “Nonlinear Schroedinger evolution equations”, Nonlinear Analysis Theory, Methods and Applications, 4 (1980), 667 | DOI | MR

[45] C. Foias, G. Prodi, “Sur le comportement global des solutions non : tationnaires des equations de Navier–Stokes en dimension $2$”, Rend. Sem. Mat. Univ. Padova, 39 (1967), 1–34 | MR | Zbl

[46] A. V. Babin, M. I. Vishik, “Otsenki sverkhu i snizu razmernosti attraktorov evolyutsionnykh uravnenii”, SMZh, 1983, no. 5 | MR

[47] Yu. S. Ilyashenko, “O razmernosti attraktorov $k$-szhimayuschikh sistem v beskonechnomernom prostranstve”, Vestnik MGU, ser. matem. mekh., 1983, no. 3 | MR