On some boundary value problems for a class of hyperbolic systems of second order in conic domains

For one class of hyperbolic systems of second order, we consider multidimensional versions of the Darboux problem in conic domains. A priori estimates of solutions of these problems are obtained. The existence of a solution of the Darboux problems is proved under the supplementary conditions imposed on the coefficients of the system, when the data support of the problem is of temporary type.