A problem with a~Frankl condition on the boundary of the ellipticity domain for the Gellerstedt equation with a~singular coefficient
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2012), pp. 61-66.

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We study a problem with the Frankl and Bitsadze–Samarskii conditions on the elliptic boundary and on the degeneration line for the Gellerstedt equation with a singular coefficient. We prove the correctness of the stated problem.
Mots-clés : unique solvability, existence of solution, singular coefficient.
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Mirsaburova Gulnora. A problem with a~Frankl condition on the boundary of the ellipticity domain for the Gellerstedt equation with a~singular coefficient. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2012), pp. 61-66. https://geodesic-test.mathdoc.fr/item/IVM_2012_1_a7/

[1] Frankl F. I., “Obtekanie profilei gazom dozvukovoi skorosti so sverkhzvukovoi zonoi, okanchivayuscheisya pryamym skachkom uplotneniya”, Prikl. matem. i mekhan., 20:2 (1956), 196–202 | MR | Zbl

[2] Lin Tszyan-bin, “O nekotorykh zadachakh Franklya”, Vestn. LGU. Ser. matem., mekhan. i astr., 1961, no. 3(13), 28–39 | Zbl

[3] Devingtal Yu. V., “O suschestvovanii i edinstvennosti resheniya odnoi zadachi F. I. Franklya”, Izv. vuzov. Matem., 1958, no. 2, 39–51 | MR | Zbl

[4] Salakhitdinov M. S., Mirsaburov M., Nelokalnye zadachi dlya uravnenii smeshannogo tipa s singulyarnymi koeffitsientami, Universitet “Yangiyo'l poligraf servis”, Tashkent, 2005

[5] Bitsadze A. V., Samarskii A. A., “O nekotorykh prosteishikh obobscheniyakh lineinykh ellipticheskikh kraevykh zadach”, DAN SSSR, 185:4 (1969), 739–740 | Zbl

[6] Mirsaburov M., “Kraevaya zadacha dlya odnogo klassa uravnenii smeshannogo tipa s usloviem Bitsadze–Samarskogo na parallelnykh kharakteristikakh”, Differents. uravneniya, 37:9 (2001), 1281–1284 | MR | Zbl

[7] Bitsadze A. V., Nekotorye klassy uravnenii v chastnykh proizvodnykh, Nauka, M., 1981 | MR | Zbl