Electron. J. Diff. Equ., Vol. 2011 (2011), No. 07, pp. 1-6.

Non-local problems for parabolic-hyperbolic equations with deviation from the characteristics and three type-changing lines

Abdumauvlen S. Berdyshev, Nilufar A. Rakhmatullaeva

We prove the existence and uniqueness of solutions for a partial differential equations of mixed type (parabolic-hyperbolic type). We use energy integrals and methods from integral equations to study a problem that has deviation from the characteristics and three lines where the type changes.

Submitted November 18, 2010. Published January 15, 2011.
Math Subject Classifications: 35M10.
Key Words: Parabolic-hyperbolic equation; deviation; type-changing line; integral equations.

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Abdumauvlen Suleymanovich Berdyshev
Kazakh National Pedagogical University
named later Abaj, 050062 Almaty, Kazakhstan
email: berdyshev@mail.ru
Nilufar Alisherovna Rakhmatullaeva
Institute of Mathematics and Information Technologies
Uzbek Academy of Sciences
100125 Tashkent, Uzbekistan
email: rakhmatullaeva@mail.ru

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