96-46 Davies E.B., Parnovski L.

Trapped modes in acoustic waveguides. (450K, ps) Feb 21, 96

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Abstract. We consider the Laplace operator acting on the infinite cylinder with an obstacle inside it. Boundary conditions are assumed to be Neumann. We study the existence of (embedded) eigenvalues in two cases. For two-dimentional symmetric obstacle we give both necessary and sufficient conditions for the existence of an eigenvalue. For thin nonsymmetrical obstacle parallel to the axis of the cylinder we prove that an eigenvalue always exists.

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