The integral equations of stationary problems on the diffraction of short waves at obstacles of the segment type

Abstract

A METHOD is described for reducing two-dimensional stationary problems of the diffraction of short acoustic and elastic waves at obstacles of the segment type to integral equations of the second kind. It is shown that the principle of contractive mappings is applicable to these equations when the wavelength is sufficiently short. We investigate at the same time integral equations in which the kernel depends on the absolute value of the difference between two arguments, and when the arguments vary over a finite interval, under the assumption that the Fourier transform of the kernel has a finite number of zeros and cuts in the complex plane.