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Research Papers
The floating-body problem: an integro-differential equation without irregular frequencies
N. Kuznetsov Laboratory for Mathematical Modelling of Wave Phenomena, Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, 199178, St. Petersburg, V.O., Bolshoy pr., 61 Russian Federation
Abstract:
The linear boundary value problem under consideration describes time-harmonic motion of water in a horizontal three-dimensional layer of constant depth in the presence of an obstacle adjacent to the upper side of the layer (floating body). This problem for a complex-valued harmonic function involves mixed boundary conditions and a radiation condition at infinity. Under rather general geometric assumptions the existence of a unique solution is proved for all values of the problem's nonnegative parameter related to the frequency of oscillations. The proof is based on the representation of a solution as a sum of simple- and double-layer potentials with densities distributed over the obstacle's surface, thus reducing the problem to an indefinite integro-differential equation. The latter is shown to be soluble for all continuous right-hand side terms, for which purpose S. G. Krein's theorem about indefinite equations is used.
Keywords:
potential representations, integral operators, integro-differential equation.
Received: 20.08.2018
Citation:
N. Kuznetsov, “The floating-body problem: an integro-differential equation without irregular frequencies”, Algebra i Analiz, 31:3 (2019), 170–183; St. Petersburg Math. J., 31:3 (2020), 521–531
Linking options:
https://www.mathnet.ru/eng/aa1657 https://www.mathnet.ru/eng/aa/v31/i3/p170
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Abstract page: | 183 | Full-text PDF : | 23 | References: | 25 | First page: | 5 |
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