Geodesic
The linear inverse problem for the equation of Trikomi in three-dimensional space
Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 2 (2016), pp. 12-17 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the present work the problems of correctness of a linear inverse problem for the Trikomi equation in three-dimensional space are considered. For this problem, the theorems on existence and uniqueness of the solution are proved in certain class by «$\varepsilon$-regularization» Galerkin and of successive approximations methods.
Keywords: the Trikomi equations, a linear inverse problem, correctness of solution, Galerkin «$\varepsilon$-regularization» method, method of successive approximations. 
@article{VKAM_2016_2_a1,
     author = {S. Z. Djamalov},
     title = {The linear inverse problem for the equation of {Trikomi} in three-dimensional space},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {12--17},
     year = {2016},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2016_2_a1/}
}
TY  - JOUR
AU  - S. Z. Djamalov
TI  - The linear inverse problem for the equation of Trikomi in three-dimensional space
JO  - Vestnik KRAUNC. Fiziko-matematičeskie nauki
PY  - 2016
SP  - 12
EP  - 17
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VKAM_2016_2_a1/
LA  - ru
ID  - VKAM_2016_2_a1
ER  - 
%0 Journal Article
%A S. Z. Djamalov
%T The linear inverse problem for the equation of Trikomi in three-dimensional space
%J Vestnik KRAUNC. Fiziko-matematičeskie nauki
%D 2016
%P 12-17
%N 2
%U http://geodesic.mathdoc.fr/item/VKAM_2016_2_a1/
%G ru
%F VKAM_2016_2_a1
S. Z. Djamalov. The linear inverse problem for the equation of Trikomi in three-dimensional space. Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 2 (2016), pp. 12-17. http://geodesic.mathdoc.fr/item/VKAM_2016_2_a1/

[1] Anikonov Yu. E., Nekotorye metody issledovaniya mnogomernykh obratnykh zadach dlya differentsialnykh uravnenii, Nauka, Novosibirsk, 1978, 120 pp. | MR

[2] Bubnov B. A., K voprosu o razreshimosti mnogomernykh obratnykh zadach dlya parabolicheskikh i giperbolicheskikh uravnenii, Preprint No713; Препринт No714, ВЦ СО АН СССР, Новосибирск, 1987

[3] Dzhamalov S. Z., “O korrektnosti nekotorykh nelokalnykh kraevykh zadach dlya uravneniya smeshannogo tipa pervogo roda”, Kraevye zadachi dlya neklassicheskikh uravnenii matematicheskoi fiziki, Novosibirsk, 1989, 112–114 | MR

[4] Dzhamalov S. Z., “Ob odnoi lineinoi obratnoi zadache dlya uravneniya smeshannogo tipa vtorogo roda vtorogo poryadka v trekhmernom prostranstve”, Uzbekskii matematicheskii zhurnal, 2014, no. 4, 29–35

[5] Kozhanov A. I., “Nelineinye nagruzhennye uravneniya i obratnye zadachi”, Zhurn. vychislit. matematiki i mat. fiziki, 44:4 (2004), 694–716 | MR | Zbl

[6] Sabitov K. B, Safin E. M., “Obratnaya zadacha dlya uravneniya parabolo-giperbolicheskogo tipa v pryamougolnoi oblasti”, Doklady RAN, 429:4 (2009), 451–454 | Zbl

[7] Sabitov K. B., Martemyanova N. V., “Nelokalnaya obratnaya zadacha dlya uravneniya smeshannogo tipa”, Izv. vuzov. Matematika, 2011, no. 2, 71–85 | MR | Zbl

[8] Lavrentev M. M, Romanov V. G, Vasilev V. G., Mnogomernye obratnye zadachi dlya differentsialnykh uravnenii, Nauka, Novosibirsk, 1969, 67 pp. | MR

[9] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973, 407 pp. | MR

[10] Trenogin V. A., Funktsionalnyi analiz, Nauka, M., 494 pp. | MR