On two-dimensional water waves in a canal
2003 (English)In: Comptes rendus. Mecanique, ISSN 1631-0721, Vol. 331, no 7, 489-494 p.Article in journal (Refereed) Published
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.
IdentifiersURN: urn:nbn:se:liu:diva-23100DOI: 10.1016/S1631-0721(03)00105-0Local ID: 2497OAI: oai:DiVA.org:liu-23100DiVA: diva2:243413