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Home » Issues » Archive of Issues » 2021 - 3 issue » pp. 353-364

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Kazakhstan Almaty
Year
2021
Volume
31
Issue
3
Pages
353-364
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Section Mathematics
Title Problem with data on the characteristics for a loaded system of hyperbolic equations
Author(-s) Assanova A.T.a, Zholamankyzy A.ab
Affiliations Institute of Mathematics and Mathematical Modeling, Kazakhstana, Al-Farabi Kazakh National Universityb
Abstract We consider a problem with data on the characteristics for a loaded system of hyperbolic equations of the second order on a rectangular domain. The questions of the existence and uniqueness of the classical solution of the considered problem, as well as the continuity dependence of the solution on the initial data, are investigated. We propose a new approach to solving the problem with data on the characteristics for the loaded system of hyperbolic equations second order based on the introduction new functions. By introducing new unknown functions the problem is reduced to an equivalent family of Cauchy problems for a loaded system of differential with a parameters and integral relations. An algorithm for finding an approximate solution to the equivalent problem is proposed and its convergence is proved. Conditions for the unique solvability of the problem with data on the characteristics for the loaded system of hyperbolic equations of the second order are established in the terms of coefficient's system.
Keywords loaded systems of hyperbolic equations, problem with data on the characteristics, family of Cauchy problems, algorithm, solvability criteria
UDC 517.956
MSC 35L52, 45K05
DOI 10.35634/vm210301
Received 6 July 2021
Language English
Citation Assanova A.T., Zholamankyzy A. Problem with data on the characteristics for a loaded system of hyperbolic equations, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2021, vol. 31, issue 3, pp. 353-364.
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