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Some applications of Maz'ja's uniqueness theorem to a class of linear water wave problems

Published online by Cambridge University Press:  24 October 2008

Andrew Hulme
Andrew Hulme
Affiliation:
Department of Mathematics, University of Manchester, Manchester M13 9PL
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Abstract

This paper describes a criterion which, if satisfied, guarantees uniqueness of solution for the problem involving the radiation or diffraction of small amplitude water waves by a totally submerged body. This criterion was originally stated by a Russian mathematician, V. G. Maz'ja, although his work does not appear to be widely known. For this reason a brief outline of Maz'ja's proof is given here, together with a discussion of the condition to be satisfied by the submerged body.

Maz'ja's criterion is not satisfied by all submerged bodies and so his result does not provide a general proof of uniqueness. However, the criterion is satisfied in some important cases and examples are presented here. The partial nature of this result is due entirely to the method of proof and not to any intrinsic difficulty with the underlying hydrodynamics.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 95 , Issue 1 , January 1984 , pp. 165 - 174
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

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