Nonlocal Problem for a System of Partial Differential Equations of Higher Order with Pulsed Actions

被引：7

作者：

Assanova, A. T. ^{[1
]}

Tleulessova, A. B. ^{[2
]}

机构：

[1] Inst Math & Math Modelling, Alma Ata, Kazakhstan

[2] Almaty Gumilev Eurasian Natl Univ, Inst Math & Math Modelling, Astana, Kazakhstan

来源：

UKRAINIAN MATHEMATICAL JOURNAL | 2020年 / 71卷 / 12期

关键词：

BOUNDARY-VALUE-PROBLEMS; HYPERBOLIC-EQUATIONS; WELL-POSEDNESS; SOLVABILITY;

D O I：

10.1007/s11253-020-01750-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1821 / 1842

页数：22

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