Nonlocal problem for а system of partial differential equations of higher order with pulsed actions

• Date: 2019
• Main Authors: Assanova, A. T., Tleulessova, A. B., Асанова, Анар Турмаганбеткызы, Тлеулесова, Агила Балтабаевна, Асанова, А. Т., Тлеулесова, А. Б.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 2019
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/712
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We consider a nonlocal problem for а system of partial differential equations of higher order with pulsed actions. By introducing new unknown functions, the analyzed problem is reduced to an equivalent problem formed by a nonlocal problem for impulsive system of hyperbolic equations of the second order and integral relations. We propose an algorithm for finding the solutions of the equivalent problem based on the solution of a nonlocal problem for a system of hyperbolic equations of the second order with pulsed action for fixed values of the introduced additional functions, which are then determined from the integral relations in terms of the obtained solution. Sufficient conditions for the existence of a unique solution to the nonlocal problem for an impulsive system of hyperbolic equations of the second order are obtained by method of introduction functional parameters. The algorithms for finding its solutions are constructed. Conditions for the unique solvability of a nonlocal problem for the system of partial differential equations of higher order with pulsed actions are established in terms of the coefficients of the system and boundary matrices.