The problem on conjugation on solutions of a hyperbolic system along unknown contact boundary in sector (in Ukrainian) - R. V. Andrusyak; N. O. Burdeyna; V. M. Kyrylych (Математичні Студії, 2013)
The conditions of solvability in the generalized sense of a problem with unknown breaking line of initial data for a hyperbolic quasilinear system with two independent variables in the sector were established. Applying the method of characteristics a solution of the problem is reduced to finding the fixed point of the operator whose existence and uniqueness are proved using the Banach theorem.