On the well-posedness of periodic problems for the system of hyperbolic equations with finite time delay

被引：21

作者：

Assanova, Anar T. ^{[1
]}

Iskakova, Narkesh B. ^{[1
,2
]}

Orumbayeva, Nurgul T. ^{[3
]}

机构：

[1] Inst Math & Math Modeling, Dept Differential Equat, Pushkin Str 125, Alma Ata 050010, Kazakhstan

[2] Abai Kazakh Natl Pedag Univ, Alma Ata, Kazakhstan

[3] EA Buketov Karaganda State Univ, Karagandy, Kazakhstan

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2020年 / 43卷 / 02期

关键词：

algorithm; family of periodic problems for system of differential equations with finite delay; periodic problem; system of hyperbolic equations with delayed argument; unique solvability; PARTIAL-DIFFERENTIAL-EQUATIONS; BOUNDARY-VALUE PROBLEM; STABILITY; OSCILLATION;

D O I：

10.1002/mma.5970

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A periodic problem for the system of hyperbolic equations with finite time delay is investigated. The investigated problem is reduced to an equivalent problem, consisting the family of periodic problems for a system of ordinary differential equations with finite delay and integral equations using the method of a new functions introduction. Relationship of periodic problem for the system of hyperbolic equations with finite time delay and the family of periodic problems for the system of ordinary differential equations with finite delay is established. Algorithms for finding approximate solutions of the equivalent problem are constructed, and their convergence is proved. Criteria of well-posedness of periodic problem for the system of hyperbolic equations with finite time delay are obtained.

引用

页码：881 / 902

页数：22

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