Geodesic
On an inverse problem for the multidimensional equation mixed type of the first kind of the second order with periodic conditions
Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 4 (2018), pp. 10-18 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 inverse problem for the multidimensional equation mixed type of the first kind of the second order with periodic conditions are considered. For this problem, the theorems on existence and uniqueness of the solution are proved in a certain class by "$\varepsilon$-regularization" a priori estimations and of successive approximations methods.
Keywords: The multidimensional equation mixed type of the first kind of the second order, inverse problem, correctness of solution, $\varepsilon$-method, method of successive approximations, method a priori estimations. 
@article{VKAM_2018_4_a0,
     author = {S. Z. Djamalov},
     title = {On an inverse problem for the multidimensional equation mixed type of the first kind of the second order with periodic conditions},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {10--18},
     year = {2018},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2018_4_a0/}
}
TY  - JOUR
AU  - S. Z. Djamalov
TI  - On an inverse problem for the multidimensional equation mixed type of the first kind of the second order with periodic conditions
JO  - Vestnik KRAUNC. Fiziko-matematičeskie nauki
PY  - 2018
SP  - 10
EP  - 18
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VKAM_2018_4_a0/
LA  - ru
ID  - VKAM_2018_4_a0
ER  - 
%0 Journal Article
%A S. Z. Djamalov
%T On an inverse problem for the multidimensional equation mixed type of the first kind of the second order with periodic conditions
%J Vestnik KRAUNC. Fiziko-matematičeskie nauki
%D 2018
%P 10-18
%N 4
%U http://geodesic.mathdoc.fr/item/VKAM_2018_4_a0/
%G ru
%F VKAM_2018_4_a0
S. Z. Djamalov. On an inverse problem for the multidimensional equation mixed type of the first kind of the second order with periodic conditions. Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 4 (2018), pp. 10-18. http://geodesic.mathdoc.fr/item/VKAM_2018_4_a0/

[1] Anikonov Yu. E., Nekotorye metody issledovaniya mnogomernyh obratnyh zadach dlya differencial'nyh uravnenij, Nauka, Novosibirsk, 1978, 120 pp.

[2] Bubnov B. A., K voprosu o razreshimosti mnogomernyh obratnyh zadach dlya parabolicheskih i giperbolicheskih uravnenij, Preprinty No713-714, VC SO AN SSSR, Novosibirsk, 1987

[3] Vragov V. N., Kraevye zadachi dlya neklassicheskih uravnenij matematicheskoj fiziki, NGU, Novosibirsk, 1983, 84 pp.

[4] Dzhamalov S. Z., “Ob odnoj linejnoj obratnoj zadachi dlya uravneniya Trikomi v tryohmernom prostranstve”, Vestnik KRAUNC. Fiziko-matematicheskie nauki, 2016, no. 2(13), 12-17 | MR | Zbl

[5] Dzhamalov S. Z., “Ob odnoj linejnoj obratnoj zadache dlya uravneniya smeshannogo tipa pervogo roda vtorogo poryadka v trekhmernom prostranstve”, UzMZH, 2017, no. 2, 58-65 | MR

[6] Dzhenaliev M. T., K teorii kraevyh zadach dlya nagruzhennyh differencial'nyh uravnenij, Institut teoreticheskoj i prikladnoj matematiki, Almaty, 1995

[7] Kabanihin S. I., Obratnye i nekorrektnye zadachi, Sibirskoe nauchnoe izdatel'stvo, Novosibirsk, 2009, 458 pp.

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

[9] Sabitov K. B., Martem'yanova N. V., “Nelokal'naya obratnaya zadacha dlya uravneniya smeshannogo tipa”, Izv. vuzov. Matematika, 2011, no. 2, 71-85 | Zbl

[10] Lavrent'ev M. M, Romanov V. G, Vasil'ev V. G., Mnogomernye obratnye zadachi dlya differencial'nyh uravnenij, Nauka, Novosibirsk, 1969, 67 pp.

[11] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoj fiziki, Nauka, M, 1973

[12] Nakhushev A. M., “Nagruzhennye uravneniya i ih prilozheniya”, Differenc. uravneniya, 19:1 (1983), 86-94 | MR | Zbl

[13] Cybikov B. N., “O korrektnosti periodicheskoj zadachi dlya mnogomernogo uravneniya smeshannogo tipa”, Neklassicheskie uravneniya matematicheskoj fiziki, Novosibirsk, 1986, 201-206

[14] Trinogin V. A., Funkcional'nyj analiz, Nauka, M, 1980, 494 pp.