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http://bura.brunel.ac.uk/handle/2438/2178
Title: | Boundary value problems for the Helmholtz equation in a half-plane |
Authors: | Chandler-Wilde, SN |
Issue Date: | 1994 |
Publisher: | Brunel University |
Citation: | Maths Technical Papers (Brunel University). June 1994, pp 1-10 |
Abstract: | The Dirichlet and impedance boundary value problems for the Helmholtz equation in a half-plane with bounded continuous boundary data are studied. For the Dirichlet problem the solution can be constructed explicitly. We point out that, for wavenumbers k > 0, the solution, although it satisfies a limiting absorption principle, may increase in magnitude with distance from the boundary. Using the explicit solution we propose a novel radiation condition which we utilise in formulating the impedance boundary value problem. By reformulating this problem as a boundary integral equation we prove uniqueness and existence of solution for a certain range of admissable impedance boundary data. |
URI: | http://bura.brunel.ac.uk/handle/2438/2178 |
Appears in Collections: | Dept of Mathematics Research Papers Mathematical Sciences |
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TR_11_94.pdf | 297.56 kB | Adobe PDF | View/Open |
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