Geodesic
First order hyperbolic equations with constant operator coefficients
Sbornik. Mathematics, Tome 22 (1974) no. 2, pp. 257-270 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper considers the Cauchy problem for a hyperbolic equation with constant operator coefficients in Hilbert space: $$ \frac{\partial\psi}{\partial t}=\sum_{k=1}^n A_k\frac{\partial\psi}{\partial x_k}+B\psi, $$ where $A_k$ and $B$ are selfadjoint operators and $B$ is semibounded. As an example we consider ultraparabolic systems. Bibliography: 10 titles. 
@article{SM_1974_22_2_a5,
     author = {E. A. Fadeeva},
     title = {First order hyperbolic equations with constant operator coefficients},
     journal = {Sbornik. Mathematics},
     pages = {257--270},
     year = {1974},
     volume = {22},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1974_22_2_a5/}
}
TY  - JOUR
AU  - E. A. Fadeeva
TI  - First order hyperbolic equations with constant operator coefficients
JO  - Sbornik. Mathematics
PY  - 1974
SP  - 257
EP  - 270
VL  - 22
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1974_22_2_a5/
LA  - en
ID  - SM_1974_22_2_a5
ER  - 
%0 Journal Article
%A E. A. Fadeeva
%T First order hyperbolic equations with constant operator coefficients
%J Sbornik. Mathematics
%D 1974
%P 257-270
%V 22
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1974_22_2_a5/
%G en
%F SM_1974_22_2_a5
E. A. Fadeeva. First order hyperbolic equations with constant operator coefficients. Sbornik. Mathematics, Tome 22 (1974) no. 2, pp. 257-270. http://geodesic.mathdoc.fr/item/SM_1974_22_2_a5/

[1] Yu. L. Daletskii, “Kontinualnye integraly, svyazannye s operatornymi evolyutsionnymi uravneniyami”, Uspekhi matem. nauk, XVII:5 (107) (1962), 3–115

[2] Yu. M. Berezanskii, Razlozhenie po sobstvennym funktsiyam samosopryazhennykh operatorov, izd-vo «Naukova dumka», Kiev, 1965 | MR

[3] E. Khille, R. S. Fillips, Funktsionalnyi analiz i polugruppy, IL, Moskva, 1962

[4] I. M. Gelfand, G. E. Shilov, Prostranstva osnovnykh i obobschennykh funktsii, Fizmatgiz, Moskva, 1958

[5] V. S. Vladimirov, Yu. N. Drozhzhinov, “Obobschennaya zadacha Koshi dlya ultraparabolicheskogo uravneniya”, Izv. AN SSSR, seriya matem., 31 (1967), 1341–1360 | Zbl

[6] A. M. Ilin, “Ob odnom klasse ultraparabolicheskikh uravnenii”, DAN SSSR, 159:8 (1964), 1214–1217 | MR

[7] T. G. Genchev, “Ob ultraparabolicheskikh uravneniyakh”, DAN SSSR, 151:2 (1963), 265–268 | Zbl

[8] E. A. Fadeeva, “O zadache Koshi lineinogo giperbolicheskogo uravneniya pervogo poryadka s operatornymi koeffitsientami”, Uspekhi matem. nauk, XXII:2 (134) (1967), 128–130 | MR

[9] P. Phillips, “Dissipative operators and hyperbolic systems of partial differential equations”, Trans. Amer. Math. Soc., 90:2 (1959), 193–254 | DOI | MR | Zbl

[10] Yu. L. Daletskii, E. A. Fadeeva, “Giperbolicheskie uravneniya s operatornymi koeffitsientami i ultraparabolicheskie sistemy”, Ukr. matem. zh., XXIV:1 (1972), 92–95