Dirichlet type problem for strictly hyperbolic systems of first order with constant coefficients in two dimensional domain

In this work is considered strictly hyperbolic system of first order with constant coefficients in bounded domain with piecewise boundary. That system consists eight scalar equations. It is supposed, that boundary of that domain contain eight smooth noncharacteristic arcs. Two linear combination of unknown solution of system at the boundary of domain is given. For some conditions on the coefficients of that linear combinations, boundary of domain and behavior of solution near characteristics, which pass through an edge of boundary, unique solvability of such problems is proved.