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MATHEMATICA BOHEMICA, Vol. 126, No. 2, pp. 411-420 (2001)
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# 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: ` nikuz@snark.ipme.ru`; * V. Maz'ya*, Mathematical Institute, Linköping University, S-581 83 Linköping, 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 Hölder spaces

**Classification (MSC2000):** 76B15, 35Q35

**Full text of the article:**

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