On the Dirichlet problem for the Helmholtz equation on the plane with boundary conditions on an almost closed curve
Journal Article
·
· Sbornik. Mathematics
- Institute of Mathematics with Computer Centre, Russian Academy of Sciences, Ufa (Russian Federation)
In this article the two-dimensional Dirichlet boundary-value problem is considered for the Helmholtz operator with boundary conditions on an almost closed curve {gamma}{sub {epsilon}} where {epsilon}<<1 is the distance between the end-points of the curve. A complete asymptotic expression is constructed for a pole of the analytic continuation of the Green's function of this problem as the pole converges to a simple eigenfrequency of the limiting interior problem in the case when the corresponding eigenfunction of the limiting problem has a second-order zero at the centre of contraction of the gap. The influence of symmetry of the gap on the absolute value of the imaginary parts of the poles is investigated.
- OSTI ID:
- 21202944
- Journal Information:
- Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 6 Vol. 191; ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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