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.

Key words:

• Wave diffraction
• boundary‐value problem
• impedance conditions
• pseudo‐differential operators
• Bessel potential spaces
• Besov spaces

Notes

This work was supported in part by Unidade de Investigação Matemática e Aplicações of Universidade de Aveiro through the Portuguese Science Foundation (FCT‐Fundação para a Ciência e a Tecnologia).