Acoustic scattering by several obstacles and screens with Neumann boundary condition

The Neumann problem in the exterior of several obstacles and screens (cracks) is studied for a propagative Helmholtz equation in two dimensions. The solvability of this problem is proved in the general case by the method of interior boundaries. In doing so, additional boundaries are introduced inside obstacles. The solution is obtained in the form of a non-classical angular potential on screens and single-layer potential on obstacles and additional boundaries. The problem is reduced to the integral equations containing Cauchy kernels on screens and next to the uniquely solvable Fredholm equation of the second kind on the whole boundary.