Abstract
We consider a kind of scattering problem which models the scattering of an electromagnetic time-harmonic plane wave by an infinite cylinder having an open arc and a penetrable obstacle in $R^{2}$R2 as cross section. To this end, we solve a scattering problem for the Helmholtz equation in $R^2$R2 where the scattering object is a combination of a crack Γ and a penetrable obstacle D, and we have Dirichlet-Impedance type boundary condition on Γ and transmission boundary condition on ∂D. Applying potential theory, the problem can be reformulated as a boundary integral system. We establish the existence and uniqueness of a weak solution to the system by using the modified Fredholm theory.
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