We consider a nonlocal problem for a 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 including a nonlocal problem for the impulsive system of the second-order hyperbolic equations and integral relations. We propose an algorithm for finding the solutions of the equivalent problem based on the solution of the nonlocal problem for the 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 unique solution of the nonlocal problem for an impulsive system of hyperbolic equations of the second order are obtained by method of introduction of functional parameters. The algorithms for finding its solutions are constructed. Conditions for the unique solvability of the nonlocal problem for a system of partial differential equations of higher order with pulsed actions are established in terms of the coefficients of the system and boundary matrices.

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具有脉冲作用的高阶偏微分方程系统的非局部问题

我们考虑具有脉冲作用的高阶偏微分方程系统的非局部问题。通过引入新的未知函数，将所分析的问题简化为一个等效问题，其中包括二阶双曲方程和积分关系的脉冲系统的非局部问题。我们提出了一种算法，该算法基于对引入附加函数的固定值具有脉冲作用的二阶双曲方程组的非局部问题的解，找到等效问题的解，然后从积分关系确定就得到的解决方案而言。通过引入函数参数的方法，得到了二阶双曲方程脉冲系统非局部问题唯一解存在的充分条件。构建用于寻找其解的算法。根据系统和边界矩阵的系数，建立了具有脉冲作用的高阶偏微分方程系统的非局部问题的唯一可解性条件。