We consider the spectral Neumann problem for the Laplace operator in an acoustic waveguide obtained from a straight unit strip by a low box-shaped perturbation. We prove that the waveguide supports a trapped mode with an eigenvalue embedded into the continuous spectrum. The main technical difficulty is caused by corner points of the perturbed wall.
Waveguides with a box-shaped perturbation: Eigenvalues of the Neumann problem.
DURANTE, Tiziana
2017
Abstract
We consider the spectral Neumann problem for the Laplace operator in an acoustic waveguide obtained from a straight unit strip by a low box-shaped perturbation. We prove that the waveguide supports a trapped mode with an eigenvalue embedded into the continuous spectrum. The main technical difficulty is caused by corner points of the perturbed wall.File in questo prodotto:
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