On the solvability of one boundary value problem for one class of semilinear second order hyperbolic systems

For one class of semilinear second order hyperbolic systems it is considered the Sobolev problem in the conic domain of time type which represents a multidimensional version of the Darboux second problem. The questions on global and local solvability, uniqueness, and also nonexistence of a solution to this problem are studied.