Summary
The question of uniqueness is considered for a couple of new linearized problems in the water-wave theory. The first of these problems describes the radiation and scattering of time-harmonic waves by a fixed body supported in water by an air cushion. In the second problem, the body is assumed to be freely floating. For both problems the method developed by John [2] is applied for proving the uniqueness theorems. The proof is outlined for the first problem and the result is formulated for the more complicated second problem.
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References
F. John: Comm. Pure Appl. Math. 2, 13 (1949)
F. John: Comm. Pure Appl. Math. 3, 45 (1950)
N. Kuznetsov, V. Maz’ya, B. Vainberg: Linear Water Waves: A Mathematical Approach, (Cambridge University Press, Cambridge 2002)
N. G. Kuznetsov, M. J. Simon: J. Fluid Mech. 386, 5 (1999)
J. N. Newman: ‘Diffraction of water waves by an air chamber’. In: 15th International Workshop on Water Waves and Floating Bodies, Israel, February 27-March 1, 2000, ed. by T. Miloh (University of Tel-Aviv Press, Tel-Aviv 2000)
F. Ursell: ‘Some unsolved and unfinished problems in the theory of waves’. In: Wave Asymptotics. ed. by P. A. Martin (Cambridge University Press, Cambridge 1992)
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Kuznetsov, N. (2003). On the Motion of a Floating Body Supported by an Air Cushion. In: Cohen, G.C., Joly, P., Heikkola, E., Neittaanmäki, P. (eds) Mathematical and Numerical Aspects of Wave Propagation WAVES 2003. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55856-6_77
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DOI: https://doi.org/10.1007/978-3-642-55856-6_77
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