On a non-local problem for system of partial differential equations of hyperbolic type in a specific domain


Assanova A.T. Bekbauova A.U. Talipova M.Z.
29 December 2023al-Farabi Kazakh State National University

International Journal of Mathematics and Physics
2023#14Issue 236 - 41 pp.

The non-local problem for second order system of partial differential equations of hyperbolic type is studied in the specific domain. For solving this problem we use a functional parametrization method. This method isan extension of Dzhumabaev’s parametrization method to a partial differential equations of hyperbolic type. Weintroduce a parameter-function, expressed as the unknown functions value at the characteristics t = 0 within the given domain. This transforms the nonlocal problem into an equivalent parameterized problem, involving the Gours at problem for a system of partial differential equations of hyperbolic type and an additional relation based on the functional parameter. Subsequently, starting from the additional condition and the consistency condition, we formulate the Cauchy problem for a system of differential equations with respect to the unknown parameter-function. We develop an algorithm for solving the parameterized problem and demonstrate its convergence. Additionally, we derive conditions for the existence and uniqueness of a solution to the parameterized problem. Unique solvability conditions for the nonlocal problem for second-order system of partial differential equations of hyperbolic type in a specific domain are established in terms of the initial data.

Dzhumabaev’s parametrization method , non-local problem , parameterized problem , partial differential equations of hyperbolic type , solution

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Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
K.Zhubanov Aktobe Regional University, Aktobe, Kazakhstan

Institute of Mathematics and Mathematical Modeling
K.Zhubanov Aktobe Regional University

10 лет помогаем публиковать статьи Международный издатель

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