@article{Assanova_Bekbauova_Talipova_2023, title={On a non-local problem for system of partial differential equations of hyperbolic type in a specific domain}, volume={14}, url={https://ijmph.kaznu.kz/index.php/kaznu/article/view/735}, DOI={10.26577/ijmph.2023.v14.i2.04}, abstractNote={<p>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 is an extension of &nbsp;Dzhumabaev’s parametrization method &nbsp;to a partial differential equations of hyperbolic type. We introduce a parameter-function, expressed as the unknown function’s value at the characteristics &nbsp;within the given domain. This transforms the nonlocal problem into an equivalent parameterized problem, involving the Goursat problem for a system of partial differential equations of hyperbolic type and an additional relation &nbsp;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 &nbsp;second-order system of partial differential equations of hyperbolic type in a specific domain are established in terms of the initial data.</p>}, number={2}, journal={International Journal of Mathematics and Physics}, author={Assanova, A. T. and Bekbauova, A. and Talipova, M.}, year={2023}, month={Dec.}, pages={36–41} }