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Existence of Solutions of an Ill-Posed Problem for the Vibrating String

Published online by Cambridge University Press:  20 November 2018

L. L. Campbell
L. L. Campbell*
Affiliation:
Department of Mathematics and Statistics Queen's UniversityKingston Ontario K7l 3N6, Canada
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Abstract

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The Dirichlet problem is examined for the vibrating string equation on a rectangle with commensurable sides. As is well-known, a solution, if it exists, is not unique. A necessary and sufficient condition is obtained on the boundary values for existence of solutions. A simple formula for the solution is obtained.

Keywords

35R2535C05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 1 , 01 March 1982 , pp. 29 - 36
Copyright
Copyright © Canadian Mathematical Society 1982

References

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