Diffraction by a union of strips with impedance conditions in Besov and Bessel potential spaces

Abstract

We consider an impedance boundary‐value problem for the Helmholtz equation which models a wave diffraction problem with imperfect conductivity on a union of strips. Pseudo‐differential operators acting between Bessel potential spaces and Besov spaces are used to deal with this wave diffraction problem. In particular, these operators allow a reformulation of the problem into a system of integral equations. The main result presents impedance parameters which ensure the well‐posedness of the problem in scales of Bessel potential spaces and Besov spaces.

First Published Online: 14 Oct 2010