Geodesic
A problem with local and nonlocal conditions on the boundary of the ellipticity domain for a mixed type equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2021), pp. 80-93 Cet article a éte moissonné depuis la source Math-Net.Ru

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For the Gellerstedt equation with a singular coefficient in some mixed domain, when the ellipticity boundary coincides with the segment of the Oy axis and the normal curve of the equation, the problem with the Bitsadze–Samarskii conditions on the elliptic boundary and on the degeneration line is studied. The correctness of the formulated problem is proved.
Keywords: extremum principle, uniqueness of a solution, F. Tricomi singular integral equation, kernel with a first-order singularity at an isolated singular point, Wiener–Hopf equation, index.
Mots-clés : existence of a solution 
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     title = {A problem with local and nonlocal conditions on the boundary of the ellipticity domain for a mixed type equation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {80--93},
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     url = {http://geodesic.mathdoc.fr/item/IVM_2021_12_a6/}
}
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M. Mirsaburov; N. Kh. Khurramov. A problem with local and nonlocal conditions on the boundary of the ellipticity domain for a mixed type equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2021), pp. 80-93. http://geodesic.mathdoc.fr/item/IVM_2021_12_a6/

[1] Smirnov M. M., Uravneniya smeshannogo tipa, Vyssh. shk., M., 1985

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

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

[4] Mirsaburov M., Khurramov N., “Zadacha s usloviem Bitsadze–Samarskogo na kharakteristikakh odnogo semeistva i obschimi usloviyami sopryazheniya na linii vyrozhdeniya dlya uravneniya Gellerstedta s singulyarnym koeffitsientom”, Differents. uravneniya, 56:8 (2020), 1073–1094 | Zbl

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

[6] Gakhov F. D., Cherskii Yu. I., Uravneniya tipa svertki, Nauka, M., 1978