Properties of a System of Integral Equations of the First Kind in Problems of Diffraction by a Permeable Body

We study a linear system of integral equations of the first kind arising in the problem of wave diffraction by a local permeable body. The equivalence of the system and the original boundary value diffraction problem is established. The existence and uniqueness of the solution of the system and the dissipativity of its matrix operator are proved. The questions of the existence of nonradiating currents and their relation to the properties of the matrix operator of the system are considered.