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On the two-dimensional sloshing problem
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
Lab. Math. Modelling Wave Phenomena, Inst. for Prob. in Mech. Engineering, Russian Academy of Sciences, Bol'shoy pr. 61, St Petersburg 199178, Russian Federation.
Lab. Math. Modelling Wave Phenomena, Inst. for Prob. in Mech. Engineering, Russian Academy of Sciences, Bol'shoy pr. 61, St Petersburg 199178, Russian Federation.
2004 (English)In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 460, no 2049, 2587-2603 p.Article in journal (Refereed) Published
Abstract [en]

We study an eigenvalue problem with a spectral parameter in a boundary condition. This problem for the two-dimensional Laplace equation is relevant to sloshing frequencies that describe free oscillations of an inviscid, incompressible, heavy fluid in a canal having uniform cross-section and bounded from above by a horizontal free surface. It is demonstrated that there exist domains such that at least one of the eigenfunctions has a nodal line or lines with both ends on the free surface (earlier, Kuttler tried to prove that there are no such nodal lines for all domains but his proof is erroneous). It is also shown that the fundamental eigenvalue is simple, and for the corresponding eigenfunction the behaviour of the nodal line is characterized. For this purpose, a new variational principle is proposed for an equivalent statement of the sloshing problem in terms of the conjugate stream function. © 2004 The Royal Society.

Place, publisher, year, edition, pages
2004. Vol. 460, no 2049, 2587-2603 p.
Keyword [en]
Eigenfunction, Laplace equation, Nodal domain, Nodal line, Simple eigenvalue, Sloshing problem
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-45636DOI: 10.1098/rspa.2004.1303OAI: oai:DiVA.org:liu-45636DiVA: diva2:266532
Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2017-12-13

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Kozlov, Vladimir

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