Zeitschrift für Analysis und ihre Anwendungen
Vol. 18, No. 2, pp. 297 - 305 (1999)
On the Low Wave Number Behavior of Two-Dimensional Scattering Problems for an Open Arc
R. KressR. Kress: Inst. für Num. und Ang. Math. der Univ., Lotzestr. 16-18, D - 37083 Göttingen
Abstract: The low wave number asymptotics for the solution of the Dirichlet problem for the two-dimensional Helmholtz equation in the exterior of an open arc is analyzed via a single-layer integral equation approach. It is shown that the solutions to the Dirichlet problem for the Helmholtz equation converge to a solution of the Dirichlet problem for the Laplace equation as the wave number tends to zero provided the boundary values converge.
Keywords: Helmholtz equation, exterior boundary value problems, integral equation methods, low wave number limits, cosine substitution
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Electronic fulltext finalized on: 31 Jul 2001. This page was last modified: 9 Nov 2001.