|
|||||
|
|
On the well-posedness of periodic problems for the system of hyperbolic equations with finite time delay |
|
| Authors: | Anar T Assanova Narkesh B Iskakova Nurgul T Orumbayeva |
| Institution: | 1. Department of Differential Equations, Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan;2. Department of Differential Equations, Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Abai Kazakh National Pedagogical University, Almaty, Kazakhstan;3. E.A. Buketov Karaganda State University, Karagandy, Kazakhstan |
| Abstract: | 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. |
| Keywords: | algorithm family of periodic problems for system of differential equations with finite delay periodic problem system of hyperbolic equations with delayed argument unique solvability |