Geodesic
On an inverse boundary value problem for the second order elliptic equation with additional integral condition
Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 4, pp. 30-43 
Y. T. Meqraliyev. On an inverse boundary value problem for the second order elliptic equation with additional integral condition. Vladikavkazskij matematičeskij žurnal, Tome 15 (2013) no. 4, pp. 30-43. http://geodesic.mathdoc.fr/item/VMJ_2013_15_4_a4/
@article{VMJ_2013_15_4_a4,
     author = {Y. T. Meqraliyev},
     title = {On an inverse boundary value problem for the second order elliptic equation with additional integral condition},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {30--43},
     year = {2013},
     volume = {15},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2013_15_4_a4/}
}
TY  - JOUR
AU  - Y. T. Meqraliyev
TI  - On an inverse boundary value problem for the second order elliptic equation with additional integral condition
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2013
SP  - 30
EP  - 43
VL  - 15
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VMJ_2013_15_4_a4/
LA  - ru
ID  - VMJ_2013_15_4_a4
ER  - 
%0 Journal Article
%A Y. T. Meqraliyev
%T On an inverse boundary value problem for the second order elliptic equation with additional integral condition
%J Vladikavkazskij matematičeskij žurnal
%D 2013
%P 30-43
%V 15
%N 4
%U http://geodesic.mathdoc.fr/item/VMJ_2013_15_4_a4/
%G ru
%F VMJ_2013_15_4_a4

Voir la notice de l'article provenant de la source Math-Net.Ru

An inverse boundary value problem for the second order elliptic equation with an additional first kind integral condition is investigated. First the initial problem is reduced to the equivalent problem, for which the existence and uniqueness theorem is proved. Then using these facts the existence and uniqueness of the classical solution of initial problem is proved.

[1] Tikhonov A. I., “Ob ustoichivosti obratnykh zadach”, Dokl. AN SSSR, 39:5 (1943), 195–198 | MR

[2] Lavrentev M. M., “Ob odnoi obratnoi zadache dlya volnovogo uravneniya”, Dokl. AN SSSR, 157:5 (1964), 520–521 | MR | Zbl

[3] Lavrentev M. M., Romanov V. G., Shishatskii S. T., Nekorrektnye zadachi matematicheskoi fiziki i analiza, Nauka, M., 1980, 288 pp. | MR

[4] Ivanov V. K., Vasin V. V., Tanina V. P., Teoriya lineinykh nekorrektnykh zadach i ee prilozheniya, Nauka, M., 1978, 206 pp. | MR

[5] Denisov A. M., Vvedenie v teoriyu obratnykh zadach, MGU, M., 1994, 206 pp.

[6] Solovev V. V., “Obratnye zadachi opredeleniya istochnika dlya uravneniya Puassona na ploskosti”, Zhurn. vychisl. matematiki i mat. fiziki, 44:5 (2004), 862–871 | MR | Zbl

[7] Solovev V. V., “Obratnye zadachi dlya ellipticheskikh uravnenii na ploskosti”, Dif. uravneniya, 42:8 (2006), 1106–1114 | MR | Zbl

[8] Megraliev Ya. T., “Obratnaya kraevaya zadacha dlya ellipticheskogo uravneniya vtorogo poryadka s dopolnitelnymi integralnym usloviem”, Vestn. Udmurtskogo universiteta. Matematika. Mekhanika. Kompyuternye nauki, 2012, no. 1, 32–40

[9] Megraliev Ya. T., “O razreshimosti odnoi obratnoi kraevoi zadache dlya ellipticheskogo uravneniya vtorogo poryadka”, Vestn. Tverskogo gos. un-ta. Ser. Prikl. matematika, 2011, no. 23, 25–38

[10] Prilepko A. I., Kostin A. B., “O nekotorykh obratnykh zadachakh dlya parabolicheskikh uravnenii s finalnym i integralnym nablyudeniem”, Mat. sb., 183:4 (1992), 49–68 | MR | Zbl

[11] Prilepko A. I., Tkachenko D. S., “Svoistva reshenii parabolicheskogo uravneniya i edinstvennost resheniya obratnoi zadachi ob istochnike s integralnym pereopredeleniem”, Zhurnal vychislitelnoi matematiki i mat. fiziki, 43:4 (2003), 562–570 | MR | Zbl

[12] Kamynin V. L., “Ob obratnoi zadache opredeleniya pravoi chasti v parabolicheskom uravnenii s usloviem integralnogo pereopredeleniya”, Mat. zametki, 77:4 (2005), 522–534 | DOI | MR | Zbl

[13] Sabitov K. B., Martemyanova N. V., “Nelokalnaya obratnaya zadacha dlya uravneniya elliptiko-giperbolicheskogo tipa”, Sovremennaya matematika i ee prilozheniya, 68 (2011), 40–50 | MR