Geodesic
On a~problem with shift for degenerate equation of mixed type
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2015), pp. 46-54.

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

In this paper, for a class of equations of mixed type, we consider a problem with shift on a boundary characteristic. We prove theorems of uniqueness and existence of a solution to formulated problem.
Keywords: shift condition on a bounded characteristic, uniqueness of solution, singular integral equation, isolated singularity of the first order, Wiener–Hopf equation, index of equation. 
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M. Mirsaburov; S. T. Chorieva. On a~problem with shift for degenerate equation of mixed type. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2015), pp. 46-54. http://geodesic.mathdoc.fr/item/IVM_2015_4_a4/

[1] Smirnov M. M., Uravneniya smeshannogo tipa, Vyssh. shkola, M., 1985 | MR

[2] Zhegalov V. I., “Kraevaya zadacha dlya uravneniya smeshannogo tipa s granichnymi usloviyami na perekhodnoi linii”, Uchen. zap. Kazansk. un-ta, 122, no. 3, 1962, 3–16 | MR | Zbl

[3] Nakhushev A. M., “O nekotorykh kraevykh zadachakh dlya giperbolicheskikh uravnenii i uravnenii smeshannogo tipa”, Differents. uravneniya, 5:1 (1969), 44–59 | Zbl

[4] Kapustin N. Yu., Sabitov K. B., “O reshenii odnoi problemy v teorii zadachi Franklya dlya uravnenii smeshannogo tipa”, Differents. uravneniya, 27:1 (1991), 60–68 | MR | Zbl

[5] Sabitov K. B., Isyangildin A. Kh., “Zadacha Trikomi s nelokalnym usloviem sopryazheniya dlya odnogo uravneniya smeshannogo tipa”, Dokl. RAN, 326:5 (1992), 787–791 | MR | Zbl

[6] Sabitov K. B., Isyangildin A. Kh., “Zadacha Trikomi s nelokalnym usloviem sopryazheniya dlya obobshennogo uravneniya Trikomi”, Differents. uravneniya, 32:3 (1996), 409–412 | MR | Zbl

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

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

[9] Mirsaburova Gulbakhor M., “Kombinirovannaya zadacha s usloviyami Trikomi i Franklya dlya uravneniya Gellerstedta s singulyarnym koeffitsientom”, Izv. vuzov. Matem., 2013, no. 7, 16–30 | MR | Zbl

[10] Soldatov A. P., “K neterovosti teorii operatorov. Odnomernye singulyarnie operatory obschego vida”, Differents. uravneniya, 14:4 (1978), 706–718 | MR | Zbl

[11] Duduchava R. V., Integralnye uravneniya tipa svertki s razryvnymi predsimvolami. Singulyarnye integralnye uravneniya s nepodvizhnymi osobennostyami i ikh prilozheniya k zadacham mekhaniki, Mitsniereba, Tbilisi, 1978

[12] Polosin A. A., “Ob odnoznachnoi razreshimosti zadachi Trikomi dlya spetsialnoi oblasti”, Differents. uravneniya, 32:3 (1996), 394–401 | MR | Zbl

[13] Mirsaburov M., “Kraevaya zadacha dlya odnogo klassa uravnenii smeshannogo tipa s usloviem Bitsadze–Samarskogo na parallelnykh kharakteristikakh”, Differents. uravneniya, 39:9 (2001), 1281–1284 | MR

[14] Mikhlin S. G., “Ob integralnom uravnenii F. Trikomi”, DAN SSSR, 59:6 (1948), 1053–1056

[15] Sabitov K. B., Bikkulova G. G., Gimaltdinova A. A., K teorii uravnenii smeshannogo tipa s dvumya liniyami izmeneniya tipa, Gilem, Ufa, 2006

[16] Gakhov F. D., Cherskii Yu. I., Uravneniya tipa svertki, Nauka, M., 1978 | MR | Zbl