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In this paper, we study the Helmholtz equation in a non-smooth inclusion, i.e., in a doubly connected bounded domain B in R2 with boundary ∂B that consists of two disjoint closed curves Γ and Γ0. The existence and uniqueness of a solution to the Helmholtz equation for mixed boundary conditions on Γ are obtained by using Riesz–Fredholm theory.
In this paper we consider the scattering of an electromagnetic time-harmonic plane wave by an infinite cylinder having an open arc in R2 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 λ. Applying potential theory, the problem can be reformulated as a boundary integral system. We...
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