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

Rainer Kreß | Zendy

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

Author(s) -

Rainer Kreß

Publication year - 1999

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/883

Subject(s) - helmholtz equation , laplace's equation , mathematics , mathematical analysis , dirichlet problem , dirichlet's principle , dirichlet boundary condition , wave equation , boundary value problem , scattering , integral equation , dirichlet distribution , physics , quantum mechanics

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 singlelayer 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.

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