On a problem with conditions on characteristics and free surface for a hyperbolic system of equations with three independent variables with two-fold characteristics

The existence and uniqueness of the solution of a boundary value problem with conditions on two characteristic planes and on a plane that is not a characteristic for a system of hyperbolic equations with multiple characteristics are proved. An analogue of the Riemann-Hadamard method is developed for this 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.