Geodesic
A mixed problem with Tricomi and Frankl conditions for the Gellerstedt equation with a~singular coefficient
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2013), pp. 16-30.

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

We consider a generalized Tricomi equation with a singular coefficient. For this equation in a mixed domain we study the corresponding problem, where a part of the boundary characteristic is free of boundary conditions; the deficient Tricomi condition is equivalently substituted by a nonlocal Frankl condition on a segment of the degeneration line. We prove that the stated problem is well-posed.
Keywords: gluing condition, uniqueness of solution, Tricomi singular integral equation, isolated singularity of the first order, Wiener–Hopf equation, index
Mots-clés : residue. 
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     title = {A mixed problem with {Tricomi} and {Frankl} conditions for the {Gellerstedt} equation with a~singular coefficient},
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Gulbakhor M. Mirsaburova. A mixed problem with Tricomi and Frankl conditions for the Gellerstedt equation with a~singular coefficient. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2013), pp. 16-30. http://geodesic.mathdoc.fr/item/IVM_2013_7_a1/

[1] Frankl F. I., “Obtekanie profilei gazom s mestnoi sverkhzvukovoi zonoi, okanchivayuscheisya pryamym skachkom uplotneniya”, PMM, 20:2 (1956), 196–202 | MR | Zbl

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

[3] Babenko K. I., K teorii uravnenii smeshannogo tipa, Diss. $\dots$ dokt. fiz.-matem. nauk, 1952

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

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

[6] Karatoprakliev G., “Ob odnom obobschenii zadachi Trikomi”, DAN SSSR, 158:2 (1964), 271–274 | MR

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

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

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

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

[11] Mirsaburova G., “Zadacha s analogami uslovii Franklya i Bitsadze–Samarskogo dlya uravneniya Gellerstedta”, Izv. vuzov. Matem., 2011, no. 3, 60–68 | MR

[12] Mirsaburova G., “Zadacha s usloviem Franklya na granitse oblasti elliptichnosti dlya uravneniya Gellerstedta s singulyarnym koeffitsientom”, Izv. vuzov. Matem., 2012, no. 1, 61–66 | MR | Zbl

[13] Mirsaburova G., “Ob'edinennaya zadacha Trikomi i zadacha so smescheniem dlya uravneniya Gellerstedta”, Izv. vuzov. Matem., 2012, no. 9, 32–46 | Zbl