Asymptotic behaviour of an eigenvalue in the continuous spectrum of a narrowed waveguide

作者：Cardone G^*; Nazarov S A; Ruotsalainen K

来源：Sbornik: Mathematics , 2012, 203(2): 153-182.

DOI：10.1070/SM2012v203n02ABEH004217

• acoustic waveguide
• water waves in a channel
• eigenvalues in the continuous spectrum
• asymptotic behaviour
• augmented scattering matrix

The existence of an eigenvalue embedded in the continuous spectrum is proved for the Neumann problem for Helmholtz%26apos;s equation in a two-dimensional waveguide with two outlets to infinity which are half-strips of width 1 and 1 - epsilon, where epsilon %26gt; 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.

• 出版日期2012