Well-posedness of a periodic boundary value problem for the system of hyperbolic equations with delayed argument

Abstract

The periodic boundary value problem for the system of hyperbolic equations with delayed argument is considered. By method of introduction a new functions the investigated problem reduce to an equivalent problem, consisting the family of periodic boundary value problem for a system of differential equations with delayed argument and integral relations. Relationship of periodic boundary value problem for the system of hyperbolic equations with delayed argument with the family of periodic boundary value problems for the system of ordinary differential equations with delayed argument is established. Algorithms for finding solutions of the equivalent problem are constructed and their convergence is proved. Sufficient and necessary conditions of well - posedness of periodic boundary value problem for the system of hyperbolic equations with delayed argument are obtained.