Eigenvalues oF The Laplace Operator With The Neumann Conditions At Regular Perturbed Walls oF A Waveguide

It is shown that, under an appropriate choice of local smooth perturbations of the strip sides of an acoustic waveguide with rigid walls, it is possible to form an eigenvalue disseminated into the continuous spectrum near any given inner threshold. The eigenvalue is looked for by asymptotic analysis of some auxiliary object, the augmented scattering matrix that serves as an identifier of trapped waves. Bibliography: 38 titles. Illustrations: 2 Figures. © 2011 Springer Science+Business Media, Inc.