Geodesic
A combined Tricomi problem and a~problem with a~shift for the Gellerstedt equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2012), pp. 32-46.

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We study a combined statement of the F. Tricomi problem and that with a shift by V. I. Zhegalov and A. M. Nakhushev for the Gellerstedt equation with a singular coefficient. We prove the uniqueness of its solution with the help of the extremum principle and do its existence by the method of integral equations.
Keywords: uniqueness of a solution, F. Tricomi integral equation with a shift, Wiener–Hopf equation, index of equation. 
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Gulbakhor Mirsaburova. A combined Tricomi problem and a~problem with a~shift for the Gellerstedt equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2012), pp. 32-46. http://geodesic.mathdoc.fr/item/IVM_2012_9_a3/

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

[2] Zhegalov V. I., “Kraevaya zadacha dlya uravneniya smeshannogo tipa s granichnymi usloviyami na obeikh kharakteristikakh i s razryvami na prokhodnoi 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] Smirnov M. M., Uravneniya smeshannogo tipa, Vyssh. shkola, M., 1985 | MR

[5] Mirsaburova G. M., “Zadacha Trikomi–Nakhusheva”, Mezhdunar. konf. “Differentsialnye uravneniya i topologiya”, posvyaschennaya 100-letiyu so dnya rozhdeniya Lva Semenovicha Pontryagina (1908–1988) (Moskva, 17–22 iyunya 2008 g.), Tezisy dokl., Izd-vo MGU, M., 2008, 162–163

[6] Bitsadze A. V., Nekotorye klassy uravnenii v chastnykh proizvodnykh, Nauka, M., 1981 | 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] Mikhlin S. G., “Ob integralnom uravnenii F. Tricomi”, DAN SSSR, 59:6 (1948), 1053–1056 | MR

[9] Smirnov M. M., “Obobschennoe uravnenie Trikomi”, Uchen. zap. Belorussk. gos. un-ta. Ser. fiz.-matem. nauk, 1951, no. 12, 3–9

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

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

[12] 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

[13] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady, Nauka, M., 1981 | MR | Zbl