MATHEMATICA BOHEMICA, Vol. 126, No. 2, pp. 411-420 (2001)

Water-wave problem for a vertical shell

Nikolay Kuznetsov, Vladimir Maz'ya

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:; V. Maz'ya, Mathematical Institute, Linköping University, S-581 83 Linköping, Sweden, e-mail:

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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