The Scattering Problems For Two Partially Coated Obstacles

In this paper, we consider the scattering problem of an electromagnetic plane wave by two disjoint perfectly conducting infinite cylinders in R2,which are partially coated by material with different surface impedance λ1and λ2,respectivly. Let D1and D2denote the cross section with smooth bounded boundary such that R2\(Di∪D2) is connected. The scattering problem can by attributed to the exterior mixed boundary value be Helmholtz equation in R2. We can suppose that (?)D1can divided into two parts ΓD and ΓN, that is (?)D1=ΓD∪ΓN, Given f∈H1/2(ΓD), g∈H-1/2(ΓN)), h∈H-1/2((?)D2), find u∈H1(R2\(D1U D2)) such that And the scattered field u is required to satisfy the well-known Sommerfeld Radiation condition uniformly in x=x/|x|with r=|x|.We are dedicated to research the existence and uniqueness of solution of the above direct problem.Firstly, we can obtain the uniqueness of solution by Rellich’s lemma. Secondly,we establish a boundary integral system according to an applica-tion of Green’s representation formula and potential theory, and then we use the Fredholm theory to prove the existence and uniqueness of solution. Finally, the existence of solution to the original problem are obtained.