Geodesic
Water-wave problem for a vertical shell
Mathematica Bohemica, Tome 126 (2001) no. 2, pp. 411-420.

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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.
DOI : 10.21136/MB.2001.134028
Classification : 35Q35, 76B15, 76M25
Keywords: 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 
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Kuznetsov, Nikolay; Maz'ya, Vladimir. Water-wave problem for a vertical shell. Mathematica Bohemica, Tome 126 (2001) no. 2, pp. 411-420. doi : 10.21136/MB.2001.134028. http://geodesic.mathdoc.fr/articles/10.21136/MB.2001.134028/

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