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A remark on the equation of a vibrating plate

Published online by Cambridge University Press:  14 November 2011

Andreas Stahel
Affiliation:
Mathematisches Institut, Universität Zürich, Rämistrasse 74, CH-8001 Zürich, Switzerland

Synopsis

We consider the von Karman equations, which describe a vibrating plate either with a clamped boundary or with completely free boundary. In both cases we obtain a unique, classical solution. As the main tool we use a set of integral equations, which we deduce from the well known “variations of constants” formula.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1987

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References

1Brenner, P. and Wahl, W. von. Global classical solutions of nonlinear wave equations. Math. Z. 176 (1981), 87121.CrossRefGoogle Scholar
2Grisvard, P.. Caracterisation de quelques espaces d'interpolation. Arch. Rational Mech. Anal. 25 (1967), 4063.CrossRefGoogle Scholar
3Landau, L. D. and Lifschitz, E. M.. Lehrbuch der theoretischen Physik vii (Berlin: Akademie, 1975).Google Scholar
4Taylor, M.. Pseudodifferential Operators (Princeton: Princeton University Press, 1981).Google Scholar
5Triebel, H.. Interpolation Theory, Function Spaces, Differential Operators (Amsterdam: North Holland, 1978).Google Scholar
6Wahl, W. von. On nonlinear evolution equations in a Banach space and on nonlinear vibrations of the clampled plate. Bayreuth. Math. Schr. 7 (1981), 193.Google Scholar
7Wahl, W. von. Corrections to my paper: … (see [6]). Bayreuth. Math. Schr. 20 (1985), 205209.Google Scholar
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