Trapped modes in a waveguide with a thick obstacle

Details Trapped modes in a waveguide with a thick obstacle Trapped modes in a waveguide with a thick obstacle

2001-11-08

arxiv.org/abs/math/0111103v1

Mathematics

Analysis of PDEs

17 pages, 3 figures

Scientific paper

We consider two-dimensional waveguide with a rectangular obstacle symmetric about the axis of the waveguie. We study the behaviour of the Neumann eigenvalues located below the first threshold when the sides of the obstacle approach the edges of the waveguide. We show that only one of the eigenvalues converge to the first threshold, and the rate of convergence depends on whether the length of the obstacle divided by the width of the waveguide is integer or not.

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