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Curvature-induced resonances in a two-dimensional Dirichlet tube. (English) Zbl 0838.35091

The scattering theory for a Laplacian on an infinite, planar, curved strip with Dirichlet boundary conditions is studied. The investigation is motivated by questions in the theory of quantum- and electromagnetic wave guides. Existence and asymptotic completeness of the wave operators as well as existence of resonances is established. Furthermore, the authors show that in first-order perturbation theory the imaginary part of the resonances vanish exponentially in the width of the strip.
Reviewer: J.Asch (Marseille)

MSC:

35P25 Scattering theory for PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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References:

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