The problem of scattering by a partially coated crack

In this paper we consider the scattering of an electromagnetic time-harmonic plane wave by an infinite cylinder having an open arc in R2R2 as the cross section. We assume that the arc is divided into two parts, and one of the two parts is (possibly) coated on one side by a material with surface impedance λλ. 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.