Adyghe Int. Sci. J. Vol. 22, No 2. P. 11-20. ISSN 1726-9946

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DOI: https://doi.org/10.47928/1726-9946-2022-22-2-11-20

MATHEMATICS

MSC 32A10; 32A37

Original article

Resolution of the boundary value problem for a mixed equation of the fourth order

Ashirmet Bekievich Bekiev
Associate Professor of the Department of Applied Mathematics and Informatics, Karakalpak State University named after Berdakh (Nukus, 61 2236047, Uzbekistan), Candidate of Physical and Mathematical Sciences, ashir1976@mail.ru
Rakhim Muhammetovich Shikhiyev
Assistant of the Department of Applied Mathematics and Informatics, Karakalpak State University named after Berdakh (Nukus, 61 2236047, Uzbekistan), raximm82@gmail.com

Abstract. The study of boundary value problems for high-order partial differential equations plays an important role, because many scientific and practical studies lead to boudary value problems for fourth-order partial differential equtions. In this work in a rectangular region for a fourth-order equation, a boundary value problem is considered. A criterion for the uniqueness and existence of a solution to a boundary value problem for a fourth-order equation is established. The solution is constructed as the sum of a series in terms of eigenfunctions of the corresponding spectral problem. The stability of the solution of this problem is proved.

Keywords: fourth-order equation, boundary value problem, uniqueness, existence, stability

Acknowledgments: the authors are thankful to the anonymous reviewer for his valuable remakes.
Conflict of interest: the authors declare no conflict of interest.

For citation. A. B. Bekiev, R. M. Shihiev Resolution of the boundary value problem for a mixed equation of the fourth order. Adyghe Int. Sci. J. 2022. Vol. 22, No. 2. P. 11–20. 
DOI: https://doi.org/10.47928/1726-9946-2022-22-2-11-20

The authors have read and approved the final version of the manuscript.
Submitted 01.05.2022; approved after reviewing 07.06.2022; accepted for publication 15.06.2022.

© Bekiev A. B., Shikhiev R. M., 2022

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