Pseudo-Differential Operators in a Wave Diffraction Problem with Impedance Conditions

Mathematics Subject Classification: 35J05, 35J25, 35C15, 47H50, 47G30We consider an impedance boundary-value problem for the Helmholtz equation which models a wave diffraction problem with imperfect conductivity on a strip. Pseudo-differential operators are used to deal with this wave diffraction problem. Therefore, single and double layer potentials allow a reformulation of the problem into a system of integral equations. By using operator theoretical methods, the well-posedness of the problem is obtained for a set of impedance parameters, and in a framework of Bessel potential spaces.∗ This work is partially supported by the Portuguese Science Foundation (FCT–Fundação para a Ciência ea Tecnologia) through Unidade de Investigação Matemática e Aplicações of the University of Aveiro, Portugal. * The second author is supported by the Portuguese Science Foundation through grant number SFRH/BPD/20524/2004