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.