On a Nonlocal Problem with Integral Conditions for the System of Hyperbolic Equations

Abstract

A nonlocal problem with integral conditions is considered for the system of partial differential equations of the hyperbolic type in a rectangular domain. Sufficient conditions are established for the existence of the unique classical solution of the studied problem in terms of initial data. An algorithm is proposed for finding a sequence of approximate solutions convergent to the exact solution of the problem. Special cases of the problem at hand are considered as an application of the results obtained.