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|Title:||Boundary value problems for the Helmholtz equation in a half-plane|
|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.|
|Appears in Collections:||Dept of Mathematics Research Papers|
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