N. Kuznetsov, Laboratory for Mathematical Modelling of Wave Phenomena, Inst. of Problems in Mechanical Engineering, Russian Academy of Sciences, V.O., Bol'shoy pr. 61, St. Peterburg 199178, Russian Federation, e-mail: nikuz@snark.ipme.ru; V. Maz'ya, Mathematical Institute, Linkoping University, S-581 83 Linkoping, Sweden, e-mail: vlmaz@mai.liu.se
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 Holder spaces
Classification (MSC 2000): 76B15, 35Q35
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