The method of boundary integral equations for a mixed scattering problem |
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Authors: | Guozheng Yan Mao Yao |
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Institution: | Department of Math. and Appl. Math., Central China Normal Univ., Wuhan 430079, PR China |
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Abstract: | In this paper we consider the scattering of an electromagnetic time-harmonic plane wave by an infinite cylinder having an open arc and a bounded domain in R2 as cross section. To this end, we solve a scattering problem for the Helmholtz equation in R2 where the scattering object is a combination of a crack Γ and a bounded obstacle D, and we have Dirichlet-impedance type boundary condition on Γ and Dirichlet boundary condition on ∂D (∂D∈C2). Applying potential theory, the problem can be reformulated as a boundary integral system. We establish the existence and uniqueness of a solution to the system by using the Fredholm theory. |
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Keywords: | Helmholtz equation Boundary integral equation Existence and uniqueness |
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