On the Solvability of Nonlocal Boundary Value Problem for the Systems of Impulsive Hyperbolic Equations with Mixed Derivatives - Assanova, A.T. (Discontinuity, Nonlinearity, and Complexity, 2026)
A nonlocal boundary value problem for a system of impulsive hyperbolic equations at the fixed times is considered. The questions of existence, uniqueness, and construction of algorithms for finding the solutions to this problem are studied. By introducing the additional parameters as values of solutions on specific lines the considered problem is reduced to the problem consisting of the Goursat problem for a system of hyperbolic equations and the Cauchy problem for ordinary differential equations. The algorithms for finding the approximate solutions of latter problem are obtained and their convergence to the solution of original problem is proved. Conditions for existence of a unique solution to the nonlocal boundary value problem with impulse effects are set in the terms of initial data.