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.
Asymptotic behaviour of an eigenvalue in the continuous spectrum of a narrowed waveguide / Cardone, G; Nazarov, Sa; Ruotsalainen, K.. - In: SBORNIK MATHEMATICS. - ISSN 1064-5616. - 203:2(2012), pp. 153-182. [10.1070/SM2012v203n02ABEH004217]
Asymptotic behaviour of an eigenvalue in the continuous spectrum of a narrowed waveguide
Cardone G
;
2012
Abstract
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.File | Dimensione | Formato | |
---|---|---|---|
CaNaRu1SbMat.pdf
non disponibili
Dimensione
530.29 kB
Formato
Adobe PDF
|
530.29 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.