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http://bura.brunel.ac.uk/handle/2438/2190
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. |
URI: | http://bura.brunel.ac.uk/handle/2438/2190 |
Appears in Collections: | Dept of Mathematics Research Papers Mathematical Sciences |
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TR_10_94.pdf | 207.97 kB | Adobe PDF | View/Open |
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