Geodesic
The boundary-value problem for the Lavrent'ev--Bitsadze equation with unknown right-hand side
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2011), pp. 44-52.

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We study the inverse problem for the Lavrent'ev–Bitsadze equation in a rectangular domain. We construct its solution as a series in eigenfunctions for the corresponding problem on eigenvalues and establish a criterion for its uniqueness. We also prove the stability of the obtained solution.
Keywords: mixed-type equation, inverse problem, spectral method, uniqueness, stability.
Mots-clés : existence 
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K. B. Sabitov; I. A. Khadzhi. The boundary-value problem for the Lavrent'ev--Bitsadze equation with unknown right-hand side. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2011), pp. 44-52. http://geodesic.mathdoc.fr/item/IVM_2011_5_a5/

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

[2] Tikhonov A. M., “Ob ustoichivosti obratnykh zadach”, DAN SSSR, 39:5 (1943), 195–198 | MR

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

[4] Romanov V. G., Nekotorye obratnye zadachi dlya uravneniya giperbolicheskogo tipa, Nauka, Novosibirsk, 1972 | MR

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

[6] Denisov A. M., Vvedenie v teoriyu obratnykh zadach, Izd-vo MGU, M., 1994

[7] Sabitov K. B., “Kriterii edinstvennosti resheniya kraevoi zadachi dlya uravneniya smeshanno-sostavnogo tipa”, Tr. mezhdunarodn. nauch. konf. “Differentsialnye uravneniya i smezhnye problemy”, posvyasch. yubileyu akademika V. A. Ilina, v. II, Gilem, Ufa, 2008, 154–161

[8] Sabitov K. B., Safin E. M., “Obratnaya zadacha dlya uravneniya smeshannogo parabolo-giperbolicheskogo tipa v pryamougolnoi oblasti”, Izv. vuzov. Matematika, 2010, no. 4, 55–62 | Zbl

[9] Sabitov K. B., “Ob odnoi kraevoi zadache dlya uravneniya smeshannogo tipa tretego poryadka”, Dokl. RAN, 427:5 (2009), 593–596 | MR | Zbl

[10] Smirnov M. M., Uravneniya smeshannogo tipa, Nauka, M., 1970 | MR

[11] Ilin V. A., “Edinstvennost i prinadlezhnost $W_2^1$ klassicheskogo resheniya smeshannoi zadachi dlya samosopryazhennogo giperbolicheskogo uravneniya”, Matem. zametki, 17:1 (1975), 91–101 | MR | Zbl

[12] Ilin V. A., “Teorema o edinstvennosti i prinadlezhnosti klassu $W_2^1$ klassicheskogo resheniya smeshannoi zadachi dlya nesamosopryazhennogo giperbolicheskogo uravneniya v proizvolnom tsilindre”, Differents. uravneniya, 11:1 (1975), 91–101