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On two-dimensional water waves in a canal
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
2003 (English)In: Comptes rendus. Mecanique, ISSN 1631-0721, Vol. 331, no 7, 489-494 p.Article in journal (Refereed) Published
Abstract [en]

This Note deals with an eigenvalue problem that contains a spectral parameter in a boundary condition. The problem for the two-dimensional Laplace equation describes free, time-harmonic water waves in a canal having uniform cross-section and bounded from above by a horizontal free surface. It is shown that there exists a domain for which at least one of eigenfunctions has a nodal line with both ends on the free surface. Since Kuttler essentially used the non-existence of such nodal lines in his proof of simplicity of the fundamental sloshing eigenvalue in the two-dimensional case, we propose a new variational principle for demonstrating this latter fact. ⌐ 2003 AcadΘmie des sciences.

Place, publisher, year, edition, pages
2003. Vol. 331, no 7, 489-494 p.
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URN: urn:nbn:se:liu:diva-23100DOI: 10.1016/S1631-0721(03)00105-0Local ID: 2497OAI: diva2:243413
Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2011-01-13

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Kozlov, Vladimir
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