To the theory of nonlocal problems with integral conditions for systems of equations of hyperbolic type

Abstract

We consider a nonlocal problem with integral conditions for a system of hyperbolic equations of the second order. By method of introduction of functional parameters, the investigated problem is reduced to an equivalent problem formed by the Goursat problem for a system of hyperbolic equations with parameters and integral relations. Algorithms for finding approximate solutions of this problem are constructed and their convergence to the exact solution is demonstrated. Sufficient conditions for the unique solvability of the equivalent problem are obtained in terms of the initial data. Moreover, the conditions of unique solvability of the nonlocal problem with integral conditions for system of hyperbolic equations are established in terms of the coefficients of the system and kernels in the integral conditions.