Geodesic
The Gellerstedt problem for a~parabolic-hyperbolic equation of the 2nd kind
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2009), pp. 33-38.

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In this paper we consider the Gellerstedt problem for a parabolic-hyperbolic equation of the 2nd kind. We prove the unique solvability of this problem, using the representation (obtained by the author) for a solution to the modified Cauchy problem in a generalized class $R$.
Keywords: generalized solution, mixed-type equation, Gellerstedt problem, gluing conditions. 
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N. K. Mamadaliev. The Gellerstedt problem for a~parabolic-hyperbolic equation of the 2nd kind. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2009), pp. 33-38. http://geodesic.mathdoc.fr/item/IVM_2009_4_a3/

[1] Tersenov S. A., “K teorii giperbolicheskikh uravnenii s dannymi na linii vyrozhdeniya tipa”, Sib. matem. zhurn., 2:6 (1961), 913–935 | MR | Zbl

[2] Salakhitdinov M. S., Mamadaliev N. K., “Zadacha Gellerstedta dlya uravneniya parabolo-giperbolicheskogo tipa s kharakteristicheskoi liniei vyrozhdeniya”, Dokl. AN UzSSR, 1991, no. 6, 3–5 | MR

[3] Mamadaliev N. K., “Zadacha Trikomi dlya silno-vyrozhdayuschegosya uravneniya parabolo-giperbolicheskogo tipa”, Matem. zametki, 66:3 (1999), 385–392 | MR | Zbl

[4] Mamadaliev N. K., “O dvukh tozhdestvakh, svyazannykh s polucheniem predstavleniya obobschennogo resheniya giperbolicheskogo uravneniya”, Dokl. AN UzSSR, 1998, no. 10, 11–13 | Zbl

[5] Trikomi F., Integralnye uravneniya, In. lit., M., 1960, 300 pp. | MR