Geodesic
On the asymptotic behavior of solutions of quasielliptic differential equations with operator coefficients
Izvestiya. Mathematics, Tome 7 (1973) no. 6, pp. 1327-1370 
B. A. Plamenevskii. On the asymptotic behavior of solutions of quasielliptic differential equations with operator coefficients. Izvestiya. Mathematics, Tome 7 (1973) no. 6, pp. 1327-1370. http://geodesic.mathdoc.fr/item/IM2_1973_7_6_a6/
@article{IM2_1973_7_6_a6,
     author = {B. A. Plamenevskii},
     title = {On the asymptotic behavior of solutions of quasielliptic differential equations with operator coefficients},
     journal = {Izvestiya. Mathematics},
     pages = {1327--1370},
     year = {1973},
     volume = {7},
     number = {6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1973_7_6_a6/}
}
TY  - JOUR
AU  - B. A. Plamenevskii
TI  - On the asymptotic behavior of solutions of quasielliptic differential equations with operator coefficients
JO  - Izvestiya. Mathematics
PY  - 1973
SP  - 1327
EP  - 1370
VL  - 7
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/IM2_1973_7_6_a6/
LA  - en
ID  - IM2_1973_7_6_a6
ER  - 
%0 Journal Article
%A B. A. Plamenevskii
%T On the asymptotic behavior of solutions of quasielliptic differential equations with operator coefficients
%J Izvestiya. Mathematics
%D 1973
%P 1327-1370
%V 7
%N 6
%U http://geodesic.mathdoc.fr/item/IM2_1973_7_6_a6/
%G en
%F IM2_1973_7_6_a6

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

A system of differential equations on the semiaxis $T$ is considered with operator coefficients in a Hilbert space. The coefficients of the system depend on $t$ and for $t\to+\infty$ are stabilized in a certain sense. The spectrum of the limit operator consists of normal eigenvalues and is contained inside a certain double angle with opening less than $\pi$ which contains the imaginary axis. Asymptotic formulas are derived for the solution, and the contribution which a multiple eigenvalue of the limiting operator pencil makes to the asymptotic expressions is investigated.

[1] Agmort S., Nirenberg L., “Properties of solutions of ordinary differential equations in Banach space”, Comm. Pure and Appl. Math., 16:2 (1963), 121–239 | DOI | MR

[2] Kondratev V. A., “Kraevye zadachi dlya parabolicheskikh uravnenii v zamknutykh oblastyakh”, Tr. Mosk. matem. ob-va, 15, 1966, 400–451

[3] Kondratev V. A., “Kraevye zadachi dlya ellipticheskikh uravnenii v oblastyakh s konicheskimi ili uglovymi tochkami”, Tr. Mosk. matem. ob-va, 16, 1967, 209–292

[4] Pazy A., “Asymptotic Expansions of Solutions of Ordinary Differential Equations in Hilbert Space”, Arch. Rat. Mech. and Analysis, 24:3 (1967), 193–218 | DOI | MR | Zbl

[5] Sternin B. Yu., “Kvaziellipticheskie uravneniya v beskonechnom tsilindre”, Dokl. AN SSSR, 194:5 (1970), 1025–1028 | MR | Zbl

[6] Evgrafov M. A., “Struktura reshenii eksponentsialnogo rosta dlya nekotorykh operatornykh uravnenii”, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 60, 1961, 145–180 | MR | Zbl

[7] Mazya V. G., Plamenevskii B. A., “Ob asimptotike reshenii differentsialnykh uravnenii s operatornymi koeffitsientami”, Dokl. AN SSSR, 196:3 (1971), 512–515

[8] Mazya V. G., Plamenevskii B. A., “Ob asimptoticheskom povedenii reshenii differentsialnykh uravnenii v gilbertovom prostranstve”, Izv. AN SSSR. Ser. matem., 36:5 (1972), 1080–1133 ; 37:3 (1973), 709–710 | MR | Zbl

[9] Plamenevskii B. A., “Ob asimptotike reshenii differentsialnykh uravnenii v banakhovom prostranstve”, Dokl. AN SSSR, 202:1 (1972), 34–37 | MR | Zbl

[10] Plamenevskii B. A., “O suschestvovanii i asimptotike reshenii differentsialnykh uravnenii s neogranichennymi operatornymi koeffitsientami v banakhovom prostranstve”, Izv. AN SSSR. Ser. matem., 36 (1972), 1348–1401 ; 37 (1973), 959 | MR | Zbl | MR | Zbl

[11] Plamenevskii B. A., “Ob asimptotike reshenii obschikh kraevykh zadach dlya kvaziellipticheskikh uravnenii v tsilindre”, Uspekhi matem. nauk, 27:6 (1972), 247–248 | MR | Zbl

[12] Agranovich M. S., Vishik M. I., “Ellipticheskie zadachi s parametrom i parabolicheskie zadachi obschego vida”, Uspekhi matem. nauk, 19:3 (1964), 53–161 | Zbl

[13] Gokhberg I. Ts., Krein M. G., Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov, Nauka, M., 1966

[14] Calderon A. P., “Uniqueness in the Caiuchy problem for partial differential equations”, Amer. J. Math., 80:1 (1958), 16–36 | DOI | MR | Zbl

[15] Krein S. G., Lineinye differentsialnye uravneniya v banakhovom prostranstve, Nauka, M., 1967 | MR

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

[17] Vazov V., Asimptoticheskie razlozheniya reshenii obyknovennykh differentsialnykh uravnenii, Mir, M., 1968