Geodesic
Exponentially splittable hyperbolic systems with two independent variables
Sbornik. Mathematics, Tome 61 (1988) no. 2, pp. 335-349 
R. K. Romanovskii. Exponentially splittable hyperbolic systems with two independent variables. Sbornik. Mathematics, Tome 61 (1988) no. 2, pp. 335-349. http://geodesic.mathdoc.fr/item/SM_1988_61_2_a4/
@article{SM_1988_61_2_a4,
     author = {R. K. Romanovskii},
     title = {Exponentially splittable hyperbolic systems with two independent variables},
     journal = {Sbornik. Mathematics},
     pages = {335--349},
     year = {1988},
     volume = {61},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_61_2_a4/}
}
TY  - JOUR
AU  - R. K. Romanovskii
TI  - Exponentially splittable hyperbolic systems with two independent variables
JO  - Sbornik. Mathematics
PY  - 1988
SP  - 335
EP  - 349
VL  - 61
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1988_61_2_a4/
LA  - en
ID  - SM_1988_61_2_a4
ER  - 
%0 Journal Article
%A R. K. Romanovskii
%T Exponentially splittable hyperbolic systems with two independent variables
%J Sbornik. Mathematics
%D 1988
%P 335-349
%V 61
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1988_61_2_a4/
%G en
%F SM_1988_61_2_a4

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

A property of hyperbolic systems which is an analogue of the property of exponential dichotomy for ordinary differential equations is studied. Exponentially decaying Green matrices of first and second kind are the main tool. Bounded solutions of e-splittable systems and projections in phase space of the Cauchy problem which describe the dichotomy of the solutions are constructed; the equivalence of the properties of e-splittability and regularity and preservation of e-splittability under small perturbations of the system are established. Bibliography: 11 titles.

[1] Massera Kh., Sheffer Kh., Lineinye differentsialnye uravneniya i funktsionalnye prostranstva, Mir, M, 1970 | MR | Zbl

[2] Kharman R., Obyknovennye differentsialnye uravneniya, Mir, M., 1970 | MR

[3] Krasnoselskii M. L., Burd V. Sh., Kolesov Yu. S., Nelineinye pochti periodicheskie kolebaniya, Nauka, M., 1970 | MR

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

[5] Petrovskii I. G., Lektsii ob uravneniyakh s chastnymi proizvodnymi, GITTL, M., 1953

[6] Pontryagin L. S., Obyknovennye differentsialnye uravneniya, Nauka, M., 1970

[7] Romanovskii R. K., “O matritsakh Rimana pervogo i vtorogo roda”, DAN SSSR, 267:3 (1982), 577–580 | MR

[8] Romanovskii R. K., “O matritsakh Rimana pervogo i vtorogo roda”, Matem. sb., 127(169) (1985), 494–501 | MR | Zbl

[9] Romanovskii R. K., “Ob ustoichivosti reshenii zadachi Koshi dlya lineinykh differentsialnykh uravnenii giperbolicheskogo tipa”, DAN SSSR, 163:5 (1965), 1077–1080 | MR | Zbl

[10] Romanovskii R. K., “Ob eksponentsialnoi dikhotomii reshenii uravnenii giperbolicheskogo tipa”, UMN, 31:1 (1976), 259–260 | MR | Zbl

[11] Romanovskii R. K., “Ob eksponentsialnoi dikhotomii reshenii odnogo klassa uravnenii v chastnykh proizvodnykh”, Tr. Vsesoyuz. konf. po uravneniyam v chastnykh proizvodnykh, Izd-vo MGU, M., 1978, 428–429