Copyright © 2009 Guozheng Yan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Consider the scattering of an electromagnetic time-harmonic plane wave by an infinite cylinder having an open crack Γ and a bounded domain D in R2 as cross section. We assume that the crack Γ is divided into two parts, and one of the two parts is (possibly) coated on one side by a material with surface impedance λ. Different boundary conditions are given on Γ and ∂D. Applying potential theory, the problem can be reformulated as a boundary integral system. We obtain the existence and uniqueness of a solution to the system by using Fredholm theory.