On the Darboux problem for a hyperbolic system of equations with multiple characteristics

The existence and uniqueness of the solution of a boundary value problem with conditions on one of the characteristics and on a free line for a system of hyperbolic equations with multiple characteristics are proved. Once an analogue of the Riemann–Hadamard method has been worked out for the specified problem, the definition of the Riemann–Hadamard matrix is given. The solution of this problem is constructed in terms of the introduced Riemann–Hadamard matrix.