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The initial value problem for a nonlinear semi-infinite string†

Published online by Cambridge University Press:  14 November 2011

R. W. Dickey
R. W. Dickey
Affiliation:
University of Wisconsin, Madison, U.S.A.
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Synopsis

The existence of a classical solution to the initial boundary value problem for a semi-infinite extensible string is proved. The result is obtained by using a Galerkin procedure on a semi-infinite interval.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 82 , Issue 1-2 , 1978 , pp. 19 - 26
Copyright
Copyright © Royal Society of Edinburgh 1978

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References

1Narasimha, R.. Non-linear vibration of an elastic string. J. Sound Vib. 8 (1968), 134–146.Google Scholar
2Dickey, R. W.. Infinite systems of nonlinear oscillation equations related to the string. Proc. Amer. Math. Soc. 23 (1969), 459–468.Google Scholar
3Nishida, T.. A note on the nonlinear vibrations of an elastic string. Mem. Fac. Engrg Kyoto Univ., 34 (1971).Google Scholar
4Nishida, T.. Nonlinear vibrations of an elastic string II, to appear.Google Scholar
5Dickey, R. W.. Infinite systems of nonlinear oscillation equations with linear damping. SIAM J. Appl. Math. 19 (1970), 208–214.Google Scholar
6Titchmarsh, E. C.. Introduction to the Theory of Fourier Integrals., 2nd edn (Oxford Univ. Press, 1948).Google Scholar
7Coddington, E. A. and Levinson, N., Theory of Ordinary Differential Equations (New York: McGraw-Hill, 1955).Google Scholar