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A new method for calculating eigenvalues with applications to gravity-capillary waves with edge constraints

Published online by Cambridge University Press:  24 October 2008

James Graham-Eagle
James Graham-Eagle
Affiliation:
Christ Church, Oxford
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Extract

The method to be described provides an alternative means of dealing with certain non-standard linear boundary-value problems. It is developed in several applications to the theory of gravity-capillary waves. The analysis is based on a variational formulation of the hydrodynamic problem, being motivated by and extending the original study by Benjamin and Scott [3].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 94 , Issue 3 , November 1983 , pp. 553 - 564
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

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[3] Benjamin, T. B. and Scott, J. C.. Gravity-capillary waves with edge constraints. J. Fluid Mech. 92 (1970), 241–267.CrossRefGoogle Scholar
[4] Lions, J. L. and Magenes, E.. Problèmes aux limites non homogènes et applications, vol. 1 (Dunod, 1968).Google Scholar
[5] Stakgold, I.. Green's Functions and Boundary Value Problems (John Wiley, 1979).Google Scholar
[6] Temme, (ed.). Nonlinear Analysis (Mathematisch Centrism, Amsterdam, 1976).Google Scholar