The Cauchy problem for Sobolev–Gal'pern type equations in spaces of functions of power growth
Sbornik. Mathematics, Tome 80 (1995) no. 2, pp. 255-269 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Results on uniqueness of solution of the Cauchy problem in the class of functions of power growth and on well-posedness of this problem in such a space are presented.
@article{SM_1995_80_2_a0,
     author = {A. L. Pavlov},
     title = {The {Cauchy} problem for {Sobolev{\textendash}Gal'pern} type equations in spaces of functions of power growth},
     journal = {Sbornik. Mathematics},
     pages = {255--269},
     year = {1995},
     volume = {80},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_80_2_a0/}
}
TY  - JOUR
AU  - A. L. Pavlov
TI  - The Cauchy problem for Sobolev–Gal'pern type equations in spaces of functions of power growth
JO  - Sbornik. Mathematics
PY  - 1995
SP  - 255
EP  - 269
VL  - 80
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1995_80_2_a0/
LA  - en
ID  - SM_1995_80_2_a0
ER  - 
%0 Journal Article
%A A. L. Pavlov
%T The Cauchy problem for Sobolev–Gal'pern type equations in spaces of functions of power growth
%J Sbornik. Mathematics
%D 1995
%P 255-269
%V 80
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1995_80_2_a0/
%G en
%F SM_1995_80_2_a0
A. L. Pavlov. The Cauchy problem for Sobolev–Gal'pern type equations in spaces of functions of power growth. Sbornik. Mathematics, Tome 80 (1995) no. 2, pp. 255-269. http://geodesic.mathdoc.fr/item/SM_1995_80_2_a0/

[1] Petrovskii I. G., Izbrannye trudy. Sistemy uravnenii s chastnymi proizvodnymi. Algebraicheskaya geometriya, Nauka, M., 1986 | MR | Zbl

[2] Gelfand I. M., Shilov G. E., Nekotorye voprosy teorii differentsialnykh uravnenii, Fizmatgiz, M., 1958 | MR | Zbl

[3] Volevich L. R., Gindikin S. G., “Zadacha Koshi i svyazannye s nei zadachi dlya uravnenii v svertkakh”, UMN, 27:4 (1972), 65–143 | MR | Zbl

[4] Gabov S. A., Sveshnikov A. G., Zadachi dinamiki stratifitsirovannykh zhidkostei, Nauka, M., 1986 | MR

[5] Uspenskii S. V., Demidenko G. V., Perepelkin V. G., Teoremy vlozheniya i prilozheniya k differentsialnym uravneniyam, Nauka, Novosibirsk, 1984 | Zbl

[6] Sobolev S. L., “Ob odnoi novoi zadache matematicheskoi fiziki”, Izv. AN SSSR. Ser. mat., 18:1 (1954), 3–50 | MR | Zbl

[7] Galpern S. A., “Zadacha Koshi dlya obschikh sistem lineinykh uravnenii s chastnymi proizvodnymi”, Tr. MMO, 9, URSS, M., 1960, 401–423 | MR | Zbl

[8] Kostyuchenko A. G., Eskin G. I., “Zadacha Koshi dlya uravnenii tipa Soboleva–Galperna”, Tr. MMO, 10, URSS, M., 1961, 273–284 | MR | Zbl

[9] Eskin G. I., “O edinstvennosti resheniya zadachi Koshi dlya uravnenii ne tipa Kovalevskoi”, Tr. MMO, 10, URSS, M., 1961, 285–295 | MR | Zbl

[10] Borok V. M., “O zadache Koshi dlya obschikh lineinykh uravnenii”, DAN SSSR, 177:4 (1967), 759–762 | MR | Zbl

[11] Borok V. M., Iokhvidovich I. Yu., “O zadache Koshi dlya obschikh lineinykh sistem”, Teoriya funktsii, funktsionalnyi analiz i ikh prilozheniya, no. 27, Kharkov, 1977, 26–33 | MR | Zbl

[12] Pavlov A. L., “O zadache Koshi dlya obschikh lineinykh uravnenii v chastnykh proizvodnykh s postoyannymi koeffitsientami”, Tezisy dokladov respublikanskoi konferentsii po nelineinym zadacham matematicheskoi fiziki, Donetsk, 1983

[13] Gramchev T. V., “Necessary and sufficient Condition for uniqueness of the characteristic cauchy problem for differential operators with constant coefficients”, Math. Nachr., 127 (1986), 309–315 | DOI | MR | Zbl

[14] Pavlov A. L., “O edinstvennosti resheniya zadachi Koshi dlya uravnenii, ne razreshennykh otnositelno starshei proizvodnoi po vremeni”, Kraevye zadachi dlya uravnenii v chastnykh proizvodnykh, Naukova Dumka, Kiev, 1978, 76–79

[15] Khërmander L., Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi. T. 2. Differentsialnye operatory s postoyannymi koeffitsientami, Mir, M., 1986

[16] Boni Zh. M., Shapira P., “Resheniya – giperfunktsii zadachi Koshi”, Matematika, 17:2 (1973), 98–106 | MR

[17] Shapira P., Teoriya giperfunktsii, Mir, M., 1972 | MR | Zbl

[18] Khartman F., Obyknovennye differentsialnye uravneniya, Mir, M., 1970 | MR | Zbl

[19] Morimoto M., “Edge of the wedge theorem and hyperfunction”, Lect. Notes Math., 287, 1972, 44–81 | MR

[20] Khërmander L., Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi. T. 1. Teoriya raspredelenii i analiz Fure, Mir, M., 1986

[21] Milnor Dzh., Osobye tochki kompleksnykh giperpoverkhnostei, Mir, M., 1971 | MR | Zbl

[22] Lyubich Yu. I., “Klassicheskoe i lokalnoe preobrazovanie Laplasa v abstraktnoi zadache Koshi”, UMN, 21:3 (1966), 3–51 | Zbl

[23] Khërmander L., “O delenii obobschennykh funktsii na polinomy”, Matematika, 3:5 (1959), 117–130

[24] Fuks B. A., Levin V. I., Funktsii kompleksnogo peremennogo i ikh prilozheniya, Gos. izd. tekh.-teor. literatury, M.–L., 1951 | MR