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Bulletin of Abai KazNPU. Series of Physical and mathematical sciences
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Vol. 79 No. 3 (2022)

ON THE APPLICATION OF A FAMILY OF BOUNDARY VALUE PROBLEMS FOR SYSTEMS OF INTEGRO-DIFFERENTIAL EQUATIONS

Published September 2022

326

121

P. Abdimanapova+−
al-Farabi Kazakh National University, Almaty Technological University, Almaty
S. Temesheva+−
al-Farabi Kazakh National University, Institute of Mathematics and Mathematical Modeling, Almaty
A. Zhumagazykyzy+−
Al-Farabi Kazakh national university
al-Farabi Kazakh National University, Almaty Technological University, Almaty
al-Farabi Kazakh National University, Institute of Mathematics and Mathematical Modeling, Almaty
Al-Farabi Kazakh national university
DOI: 10.51889/5128.2022.50.64.001
Abstract

In this paper we consider a nonlinear nonlocal boundary value problem for a system of hyperbolic equations. By introducing new unknown functions, the nonlinear nonlocal boundary value problem for a system of hyperbolic equations is reduced to an equivalent boundary value problem for the integral-differential partial differential equation.  A boundary value problem containing a family of Cauchy problems for a system of integral-differential Fredholm equations with a parameter and an unknown function is investigated using the method of introducing additional functional parameters. A modified algorithm of Jumabayev's parameterization method of finding the solution of the family of boundary value problems is proposed. Application of the parameterization method leads to a system of non-linear implicit Fredholm-type integral equations with respect to parameters. Iterative methods are used to solve this system. Sufficient conditions for the existence of an isolated solution of the considered nonlinear nonlocal boundary value problem for the system of hyperbolic equations.

pdf (Русский)
Keywords
system of hyperbolic equations, nonlinear boundary value problem, nonlocal boundary value problem, family of boundary value problems, integral-differential equation, algorithm, sufficient conditions, isolated solution
Language

Қазақ

How to Cite

[1]
Абдиманапова, П., Темешева, С. and Жумагазыкызы, А. 2022. ON THE APPLICATION OF A FAMILY OF BOUNDARY VALUE PROBLEMS FOR SYSTEMS OF INTEGRO-DIFFERENTIAL EQUATIONS. Bulletin of Abai KazNPU. Series of Physical and mathematical sciences. 79, 3 (Sep. 2022), 7–13. DOI:https://doi.org/10.51889/5128.2022.50.64.001.