Problem with nonlocal conditions on parts of the boundary characteristics and on the degeneracy segment for Gellerstedt equation with singular coefficient
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2020), pp. 64-83.

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We prove theorems of uniqueness and existence of solution of the problem with nonlocal conditions on parts of boundary characteristics and a condition of the type of the Frankl condition on the degeneracy segment of the equation for Gellerstedt equation with singular coefficient.
Mots-clés : nonlocal condition
Keywords: Frankl type condition, Tricomi singular integral equation, Wiener–Hopf equation.
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G. M. Mirsaburova. Problem with nonlocal conditions on parts of the boundary characteristics and on the degeneracy segment for Gellerstedt equation with singular coefficient. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2020), pp. 64-83. http://geodesic.mathdoc.fr/item/IVM_2020_1_a5/

[1] 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 | Zbl

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

[3] Trikomi F., O lineinykh uravneniyakh v chastnykh proizvodnykh vtorogo poryadka smeshannogo tipa, M.–L., 1947

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

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

[6] Lin Tszyan-bin, “O nekotorykh zadachakh Franklya”, Vestn. LGU. Matem., mekhan. i astronomiya, 3:13 (1961), 28–39 | Zbl

[7] Salakhitdinov M. S., Mirsaburov M., “Zadacha s nelokalnym granichnym usloviem na kharakteristike dlya odnogo klassa uravnenii smeshannogo tipa”, Matem. zametki, 86:5 (2009), 748–760 | DOI | MR | Zbl

[8] Babenko K. I., K teorii uravnenii smeshannogo tipa, Doktorskaya diss., Biblioteka matem. in-ta im. V.A. Steklova RAN, 1952

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

[10] Smirnov M. M., Uravneniya smeshannogo tipa, Vyssh. shk., M., 1985 | MR

[11] Bitsadze A. V., Nekotorye klassy uravnenii v chastnykh proizvodnykh, Nauka, M., 1981

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

[13] Duduchava R. V., Integralnye uravneniya svertki s razryvnymi predsimvolami, singulyarnye integralnye uravneniya s nepodvizhnymi osobennostyami i ikh prilozheniya k zadacham mekhaniki, Tr. Tbilissk. matem. in-ta, Tbilisi, 1979

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

[15] Mirsaburov M., “Kraevaya zadacha dlya odnogo klassa uravnenii smeshannogo tipa s usloviem Bitsadze–Samarskogo na parallelnykh kharakteristikakh”, Differents. uravneniya, 37:9 (2001), 1281–1298 | MR

[16] Mikhlin S. G., “Ob integralnom uravnenii F. Tricomi”, Dokl. AN SSSR, 59:6 (1948), 1053–1056

[17] Gakhov F. D., Cherskii Yu. N., Uravneniya tipa svertki, Nauka, M., 1978 | MR

[18] Mirsaburov M., Chorieva S. T., “Ob odnoi zadache so smescheniem dlya vyrozhdayuschegosya uravneniya smeshannogo tipa”, Izv. vuzov. Matem., 2015, no. 4, 46–54 | MR | Zbl

[19] Mirsaburov M., “Zadacha s nedostayuschim usloviem smescheniya dlya uravneniya Gellerstedta s singulyarnym koeffitsientom”, Izv. vuzov. Matem., 2018, no. 5, 52–63 | MR | Zbl