Geodesic
On unstable sets of evolution equations in the neighborhood of critical points of a stationary curve
Izvestiya. Mathematics, Tome 30 (1988) no. 1, pp. 39-70 
A. V. Babin; M. I. Vishik. On unstable sets of evolution equations in the neighborhood of critical points of a stationary curve. Izvestiya. Mathematics, Tome 30 (1988) no. 1, pp. 39-70. http://geodesic.mathdoc.fr/item/IM2_1988_30_1_a2/
@article{IM2_1988_30_1_a2,
     author = {A. V. Babin and M. I. Vishik},
     title = {On~unstable sets of evolution equations in the neighborhood of critical points of a~stationary curve},
     journal = {Izvestiya. Mathematics},
     pages = {39--70},
     year = {1988},
     volume = {30},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1988_30_1_a2/}
}
TY  - JOUR
AU  - A. V. Babin
AU  - M. I. Vishik
TI  - On unstable sets of evolution equations in the neighborhood of critical points of a stationary curve
JO  - Izvestiya. Mathematics
PY  - 1988
SP  - 39
EP  - 70
VL  - 30
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/IM2_1988_30_1_a2/
LA  - en
ID  - IM2_1988_30_1_a2
ER  - 
%0 Journal Article
%A A. V. Babin
%A M. I. Vishik
%T On unstable sets of evolution equations in the neighborhood of critical points of a stationary curve
%J Izvestiya. Mathematics
%D 1988
%P 39-70
%V 30
%N 1
%U http://geodesic.mathdoc.fr/item/IM2_1988_30_1_a2/
%G en
%F IM2_1988_30_1_a2

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

Equations of the form $\partial_t u=A(u,\lambda)$ are considered, for example, parabolic and hyperbolic equations. It is proved that the change of the local unstable invariant manifolds of such equations is determined by the form of the stationary curve $(u,\lambda)=(U(\xi),\Lambda(\xi))$, $A(u,\lambda)=0$. Bibliography: 9 titles.

[1] Babin A. V., Vishik M. I., “Attraktory evolyutsionnykh uravnenii s chastnymi proizvodnymi i otsenki ikh razmernosti”, Uspekhi matem. nauk, 38:4 (1983), 133–187 | MR | Zbl

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

[3] Shoshitaishvili A. N., “O bifurkatsii topologicheskogo tipa osobykh tochek vektornykh polei, zavisyaschikh ot parametrov”, Trudy sem. im. I. G. Petrovskogo, 4, 1975, 279–309

[4] Babin A. V., Vishik M. I., “Regular attractors of semi-groups and evolution equations”, J. Math. Pures et Appl., 62 (1983), 441–491 | MR | Zbl

[5] Babin A. V., Vishik M. I., “O statsionarnykh krivykh i neustoichivykh invariantnykh mnogoobraziyakh v okrestnosti kriticheskikh tochek evolyutsionnykh uravnenii, zavisyaschikh ot parametra”, Dokl. AN SSSR, 280:1 (1985), 19–23 | MR | Zbl

[6] Danford N., Shvarts Dzh., Lineinye operatory. Ch. 1. Obschaya teoriya, IL, M., 1962

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

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

[9] Hirsch M., Pugh C., Shub M., Invariant Manifolds, Lecture Notes in Math., 583, Springer, 1977 | MR | Zbl