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Title: Scattering by one-dimensional rough surfaces
Authors: Chandler-Wilde, SN
Ross, CR
Issue Date: 1994
Publisher: Brunel University
Citation: Maths Technical Papers (Brunel University). June 1994 , pp 1-8
Abstract: We consider the two-dimensional Dirichlet boundary value problem for the Helmholtz equation in a non-locally perturbed half-plane. We look for a solution in the form of a double-layer potential using, as fundamental solution, the Green's function for the impedance half-plane. This leads to a boundary integral equation which can be solved for any bounded and continuous boundary data provided the boundary itself does not differ too much from the flat boundary {(x1,h) ∈ R2 : x1 ∈ R} (h > 0). We show this by calculating the symbol of the integral operator in the integral equa- tion in the flat boundary case, and then using standard operator perturbation results. Continuous dependence of the solution on the shape of the boundary is shown.
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

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