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Zeitschrift für Analysis und ihre Anwendungen


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Volume 18, Issue 2, 1999, pp. 297–305
DOI: 10.4171/ZAA/883

Published online: 1999-06-30

On the Low Wave Number Behavior of Two-Dimensional Scattering Problems for an Open Arc

R. Kress[1]

(1) Georg-August-Universität Göttingen, Germany

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

Kress R.: On the Low Wave Number Behavior of Two-Dimensional Scattering Problems for an Open Arc. Z. Anal. Anwend. 18 (1999), 297-305. doi: 10.4171/ZAA/883