On the well-posedness of periodic problems for the system of hyperbolic equations with finite time delay - Assanova, A.T.; Iskakova, N.B.; Orumbayeva, N.T. (Mathematical Methods in the Applied Sciences, 2020)
A periodic problem for the systemof 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