ILL-POSED INITIAL–BOUNDARY VALUE PROBLEM FOR A SYSTEM OF MIXED-TYPE EQUATIONS WITH TWO DEGENERATE PLANES

This paper investigates an ill-posed initial–boundary value problem, in the sense of Hadamard, for a system of mixed-type equations with two degenerate planes. An appropriate correctness set is introduced for the considered problem, and sufficient conditions ensuring the uniqueness of the solution within this set are established. Furthermore, a conditional stability estimate for the solution is derived by means of appropriate a priori estimates. The obtained results contribute to the theory of ill-posed problems for systems of mixed-type equations with two degenerate planes and provide a theoretical foundation for the further investigation of boundary value problems.