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time-harmonic velocity potential; uniqueness theorem; Helmholtz equation; Neumann’s eigenvalue problem for Laplacian; integral equation method; weighted Hölder spaces; velocity potential; uniqueness; Neumann’s eigenvalue problem; Laplacian; linearized problem; radiation; scattering; time-harmonic water wave; vertical shell
The uniqueness theorem is proved for the linearized problem describing radiation and scattering of time-harmonic water waves by a vertical shell having an arbitrary horizontal cross-section. The uniqueness holds for all frequencies, and various locations of the shell are possible: surface-piercing, totally immersed and bottom-standing. A version of integral equation technique is outlined for finding a solution.
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