The existence of an eigenvalue embedded in the continuous spectrum is proved for the Neumann problem for Helmholtz's equation in a two-dimensional waveguide with two outlets to infinity which are half-strips of width 1 and 1 - epsilon, where epsilon > 0 is a small parameter. The width function of the part of the waveguide connecting these outlets is of order root epsilon; it is defined as a linear combination of three fairly arbitrary functions, whose coefficients are obtained from a certain nonlinear equation. The result is derived from an asymptotic analysis of an auxiliary object, the augmented scattering matrix.
Titolo: | Asymptotic behaviour of an eigenvalue in the continuous spectrum of a narrowed waveguide | |
Autori interni: | ||
Data di pubblicazione: | 2012 | |
Rivista: | ||
Handle: | http://hdl.handle.net/20.500.12070/4055 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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