Wave diffraction by a half-plane with an obstacle perpendicular to the boundary

We prove the unique existence of solutions for different types of boundary value problems of wave diffraction by a half-plane with a screen or a crack perpendicular to the boundary. Representations of the solutions are also obtained upon the consideration of some associated operators. This is done in a Bessel potential spaces framework and for complex (non-real) wave numbers. The investigation is mostly based on the construction of explicit operator relations, the potential method, and a factorization technique for a certain class of oscillating Fourier symbols which naturally arise from the problems.