Integral equation methods in problems of wave diffraction by a strip with higher order reactance conditions

Abstract

A problem of wave diffraction by a strip characterized with higher order reactance boundary conditions will be analysed from an integral equations viewpoint. The problem will be formulated as a boundary-transmission problem for the Helmholtz equation and in a Bessel potential space setting. Integral equations and operator theoretical methods are used to deal with the problem and, as a consequence, several convolution type equations are constructed and associated to the problem. At the end, the solvability of the problem will be discussed for a range of regularity orders of the Bessel potential spaces.