Geodesic
The Cauchy problem for singular systems of heat equations with Fredholm operator of time-derivative in Banach spaces
The Bulletin of Irkutsk State University. Series Mathematics, Tome 5 (2012) no. 2, pp. 46-54 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper matrix fundamental operator-function for singular heat operator with Fredholm operator of time-derivative is built. The formula for the generalized solution of the corresponding Cauchy problem are got.
Keywords: singular heat operator; matrix fundamental operator-function; Fredholm operator. 
@article{IIGUM_2012_5_2_a3,
     author = {O. V. Slastnaya},
     title = {The {Cauchy} problem for singular systems of heat equations with {Fredholm} operator of time-derivative in {Banach} spaces},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {46--54},
     year = {2012},
     volume = {5},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IIGUM_2012_5_2_a3/}
}
TY  - JOUR
AU  - O. V. Slastnaya
TI  - The Cauchy problem for singular systems of heat equations with Fredholm operator of time-derivative in Banach spaces
JO  - The Bulletin of Irkutsk State University. Series Mathematics
PY  - 2012
SP  - 46
EP  - 54
VL  - 5
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/IIGUM_2012_5_2_a3/
LA  - ru
ID  - IIGUM_2012_5_2_a3
ER  - 
%0 Journal Article
%A O. V. Slastnaya
%T The Cauchy problem for singular systems of heat equations with Fredholm operator of time-derivative in Banach spaces
%J The Bulletin of Irkutsk State University. Series Mathematics
%D 2012
%P 46-54
%V 5
%N 2
%U http://geodesic.mathdoc.fr/item/IIGUM_2012_5_2_a3/
%G ru
%F IIGUM_2012_5_2_a3
O. V. Slastnaya. The Cauchy problem for singular systems of heat equations with Fredholm operator of time-derivative in Banach spaces. The Bulletin of Irkutsk State University. Series Mathematics, Tome 5 (2012) no. 2, pp. 46-54. http://geodesic.mathdoc.fr/item/IIGUM_2012_5_2_a3/

[1] M. M. Vainberg, V. A. Trenogin, Teoriya vetvleniya reshenii nelineinykh uravnenii, Nauka, M., 1969, 528 pp. | MR

[2] V. S. Vladimirov, Obobschennye funktsii v matematicheskoi fizike, Nauka, M., 1979, 320 pp. | MR

[3] F. R. Gantmakher, Teoriya matrits, Nauka, M., 1966, 576 pp. | MR

[4] M. A. Krasnoselskii, P. P. Zabreiko, E. I. Pustylnik, P. E. Sobolevskii, Integralnye operatory v prostranstve summiruemykh funktsii, Nauka, M., 1966, 499 pp. | MR

[5] O. V. Korobova (Slastnaya), “Singulyarnye sistemy differentsialnykh uravnenii s neterovym operatorom pri proizvodnoi v banakhovykh prostranstvakh”, Izv. Irkut. gos. un-ta. Ser. Matematika, 1 (2007), 132–140

[6] O. V. Korobova (Slastnaya), “Zadacha Koshi dlya singulyarnoi sistemy differentsialno-raznostnykh uravnenii v banakhovykh prostranstvakh”, Intellektualnye i materialnye resursy Sibiri, Materialy region. nauch.-prakt. konf., Izd-vo BGUEP, Irkutsk, 2008, 28–32

[7] M. V. Falaleev, “Fundamentalnye operator-funktsii singulyarnykh differentsialnykh operatorov v banakhovykh prostranstvakh”, Sib. mat. zhurn., 41:5 (2000), 1167–1182 | MR | Zbl

[8] M. V. Falaleev, E. Yu. Grazhdantseva, “Fundamentalnye operator-funktsii vyrozhdennykh differentsialnykh i differentsialno-raznostnykh operatorov s neterovym operatorom v glavnoi chasti v banakhovykh prostranstvakh”, Sib. mat. zhurn., 46:6 (2005), 1393–1406 | MR | Zbl

[9] M. V. Falaleev, O. V. Korobova (Slastnaya), “Cistemy differentsialnykh uravnenii s vyrozhdeniem v banakhovykh prostranstvakh”, Sib. mat. zhurn., 49:4 (2008), 916–927 | MR | Zbl

[10] M. V. Falaleev, “Zadacha Koshi dlya vyrozhdennogo uravneniya teploprovodnosti v banakhovykh prostranstvakh”, Differents. uravneniya, 44:8 (2008), 1120–1130 | MR | Zbl

[11] M. V. Falaleev, “Fundamentalnaya operator-funktsiya vyrozhdennogo uravneniya teploprovodnosti v banakhovykh prostranstvakh”, Dokl. RAN, 416:6 (2007), 745–749 | MR | Zbl

[12] N. Sidorov, B. Loginov, A. Sinitsyn, M. Falaleev, Lyapunov–Schmidt Methods in Nonlinear Analysis and Applications, Kluwer Academic Publishers, Dordrecht, 2002, 548 pp. | MR | Zbl