Properties of the spectrum in the John problem on a freely floating submerged body in a finite basin

We consider a problem on the interaction of surface waves with a freely floating submerged body, which combines a spectral Steklov problem with a system of algebraic equations. We reduce this spectral problem to a quadratic pencil and then to the standard spectral equation for a self-adjoint operato...

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Bibliographic Details
Published in:Differential equations 2013-12, Vol.49 (12), p.1544-1559
Main Authors: Nazarov, S. A., Taskinen, J.
Format: Article
Language:English
Subjects:
Algebra
Boundary value problems
Difference and Functional Equations
Differential equations
Eigenvalues
Hilbert space
Mathematical models
Mathematical problems
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Studies
Citations: Items that this one cites
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Summary:We consider a problem on the interaction of surface waves with a freely floating submerged body, which combines a spectral Steklov problem with a system of algebraic equations. We reduce this spectral problem to a quadratic pencil and then to the standard spectral equation for a self-adjoint operator in a certain Hilbert space. In addition to general properties of the spectrum, we investigate the asymptotics of eigenvalues and eigenvectors with respect to an intrinsic small parameter.
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266113120094