Geodesic
On the identification of a linear source for the second order elliptic equation with integral condition
Trudy Instituta matematiki, Tome 21 (2013) no. 2, pp. 128-141.

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

An identification problem of the linear source for the second order elliptic equation with integral condition of the first kind is investigated. Fist 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. 
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Y. T. Mehraliyev. On the identification of a linear source for the second order elliptic equation with integral condition. Trudy Instituta matematiki, Tome 21 (2013) no. 2, pp. 128-141. http://geodesic.mathdoc.fr/item/TIMB_2013_21_2_a7/

[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. P., Nekorrektnye zadachi matematicheskoi fiziki i analiza, Nauka, M., 1980 | MR

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

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

[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”, Differents. uravneniya, 42:8 (2006), 1106–1114 | MR | Zbl

[8] Megraliev Ya. T., “Obratnaya kraevaya zadacha dlya ellipticheskogo uravneniya vtorogo poryadka”, Vestn. Bakinskogo un-ta. Ser. fiz.-mat. nauk, 2011, no. 2, 31–39

[9] Megraliev Ya. T., “Obratnaya kraevaya zadacha dlya ellipticheskogo uravneniya vtorogo poryadka s dopolnitelnymi integralnym usloviem”, Vestn. Udmurtskogo un-ta. Matematika, mekhanika, kompyuternye nauki, 2012, no. 1, 32–40

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

[11] Vabishchevich P. N., Vasil'ev V. I., Numerical solving the identification problem for the lower coefficient of parabolic equation, 22 April 2013, arXiv: 1304.5923v1 [cs.NA]

[12] Borukhov V. T., Vabischevich P. N., “Chislennoe reshenie obratnoi zadachi vosstanovleniya istochnika v parabolicheskom uravnenii”, Matematicheskoe modelirovanie, 19:11 (1988), 92–100

[13] Ionkin N. I., “Reshenie odnoi kraevoi zadachi teorii teploprovodnosti s neklassicheskimi kraevymi usloviyami”, Differents. uravneniya, 13:2 (1977), 294–304 | MR | Zbl

[14] Mehraliyev Y. T., Yusifov M. R., “The solution of a boundary value problem for a second order parabolic equation with integral conditions”, Proceedings of IMM NAS of Azerb., 30 (2009), 91–104 | MR | Zbl