Bulletin KRASEC. Phys. & Math. Sci. 2016. V. 13. no. 2. pp. 31-38. ISSN 2313-0156

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DOI: 10.18454/2313-0156-2016-13-2-31-38

MSC 35M13

SOME BOUNDARY VALUE PROBLEMS FOR A THIRD-ORDER PARABOLIC-HYPERBOLIC EQUATION IN A PENTAGONAL DOMAIN

M. Mamazhonov, S. M. Mamazhonov, Kh. B. Mamadalieva

Kokand State Pedagogical Institute. Muqimiy, 113000, Uzbekistan, Kokand, st. Amir Temur, 37

E-mail: bek84-08@mail.ru

This article is an example of application of the techniques to develop solutions of integral and differential equations. Here we consider a parabolic-hyperbolic equation (∂/∂x+∂/∂y)(Lu) = 0 in a pentagonal domain. We prove a theorem on the unique solvability of one of two given problems.

Key words: differential and integral equations, a technique for solution development, boundary value problems, parabolic-hyperbolic type, unique solvability.

References

  1. Mamazhonov M., Shermatova Kh. M., Mukadasov Kh. Postanovka i metod resheniya nekotorykh kraevykh zadach dlya odnogo klassa uravneniy tret’ego poryadka parabolo-giperbolicheskogo tipa [Statement and method of solution of some boundary value problems for one class of third-order parabolic-hyperbolic equations]. Vestnik KRAUNTs. Fiz.-mat. nauki – Bulletin KRASEC. Phys. & Math. Sci. 2014. no. 1(8). pp. 7–13.
    2. Mamazhonov M., Mamadalieva Kh. B. Statement and investigation of some boundary value problems for third-order parabolic-hyperbolic equation ¶∂/∂x (Lu) = 0 in a pentagonal domain. Bulletin KRASEC. Phys. & Math. Sci. 2016. vol. 1(12). pp. 27–34.
    3. Dzhuraev T. D., Mamazhanov M. O korrektnoy postanovke kraevykh zadach dlya odnogo klassa uravneniy tret’ego poryadka parabolo-giperbolicheskogo tipa [Correct statement of boundary value problems for one class of third-order parabolic-hyperbolic equations]. Differentsial’nye uravneniya – Differential Equations.1983. vol. 19. no. 1. pp. 37–50.
    4. Dzhuraev T. D., Sopuev A., Mamazhanov M. Kraevye zadachi dlya uravneniy parabolo-giperbolicheskogo tipa [Boundary value problems for parabolic-hyperbolic equations]. Tashkent. Fan. 1986. 220 p.

For citation: Mamazhonov M., Mamazhonov S. M., Mamadalieva Kh. B. Some boundary value problems for a third-order parabolic-hyperbolic equation in a pentagonal domain. Bulletin KRASEC. Physical and Mathematical Sciences 2016, vol. 13, no 2, 31-38. DOI: 10.18454/2313-0156-2016-13-2-31-38

Original article submitted: 05.03.16

Momag

 

Mamajonov Mirza – Ph.D. (Phys. & Math.), Associate Professor of the
Kokand Pedagogical Institute by Mukini, Uzbekistan.

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Mamazhonov Sanzharbek Mirzaevich – teacher Kokand Pedagogical Institute by Mukini, Kokand, Respublic of Uzbekistan.

 

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   Mamadalieva Khosiyatkhon Botirovna – Master of first-year physics and mathematics department of the Kokand Pedagogical Institute. Mukinje, Uzbekistan.

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