Problem with data on the characteristics for a loaded system of hyperbolic equations

Задача с данными на характеристиках для нагруженной системы гиперболических уравнений
Assanova A.T. Zholamankyzy A.
2021 Udmurt State University

Vestnik Udmurtskogo Universiteta: Matematika, Mekhanika, Kompyuternye Nauki
2021 #31 Issue 3 353 - 364 pp.

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.

Algorithm , Family of Cauchy problems , Loaded systems of hyperbolic equations , Problem with data on the characteristics , Solvability criteria

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Institute of Mathematics and Mathematical Modeling
Al-Farabi Kazakh National University

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