Unique weak solvability of a hyperbolic systems with distributed parameters on the graph

Unique solvability hyperbolic system in weak formu-lation with distributed parameters on the graph is proved. The general scheme of studies it's classical: selected functional space in which solves initial-boundary value problem and a special basis for it; for approximation of the solution of the problem are receive a priori estimates of the energy type inequalities; shows weak compactness approximations, unique and continuity of the solution on the source data. The results are fundamental in the study of problems of optimum control of a netlike industrial designs.