Enforced stability of an eigenvalue in the continuous spectrum of a waveguide with an obstacle |
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Authors: | S A Nazarov |
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Institution: | 1.Institute of Mechanical Engineering Problems,Russian Academy of Sciences,St. Petersburg,Russia |
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Abstract: | Perturbations of an eigenvalue in the continuous spectrum of the Neumann problem for the Laplacian in a strip waveguide with
an obstacle symmetric about the midline are studied. Such an eigenvalue is known to be unstable, and an arbitrarily small
perturbation can cause it to leave the spectrum to become a complex resonance point. Conditions on the perturbation of the
obstacle boundary are found under which the eigenvalue persists in the continuous spectrum. The result is obtained via the
asymptotic analysis of an auxiliary object, namely, an augmented scattering matrix. |
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Keywords: | |
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