Abstract: 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.
Keywords: time-harmonic velocity potential, uniqueness theorem, Helmholtz equation, Neumann's eigenvalue problem for Laplacian, integral equation method, weighted Hölder spaces
Classification (MSC2000): 76B15, 35Q35
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