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A uniqueness criterion for linear problems of wave-body interaction
preprint
posted on 2005-08-25, 13:13 authored by O.V. Motygin, Philip McIverThe question of uniqueness for linearized problems describing interaction
of submerged bodies with an ideal unbounded fluid is far from its final
resolution. In the present work a new criterion of uniqueness is suggested
based on Green’s integral identity and maximum principles for elliptic
differential equations. The criterion is formulated as an inequality involving
integrals of the Green function over the bodies’ wetted contours. This
criterion is quite general and applicable for any number of submerged
bodies of fairly arbitrary shape (satisfying an exterior sphere condition)
and in any dimension; it can also be generalised to more complicated
elliptic problems. Very simple bounds are also derived from the criterion,
which deliver uniqueness sets in the space of parameters defined by submergence
of the system of bodies and the frequency of oscillation. Results
of numerical investigation and comparison with known uniqueness criteria
are presented.
History
School
- Science
Department
- Mathematical Sciences
Pages
363796 bytesPublication date
2002Notes
This pre-print has been submitted, and accepted, to the journal, IMA Journal of Applied Mathematics [© Oxford University Press]. The definitive version: MOTYGIN, O.V. and McIVER, P., 2003. A uniqueness criterion for linear problems of wave-body interaction. IMA Journal of Applied Mathematics, 68(3), pp. 229-250, is available at: http://imamat.oxfordjournals.org/.Language
- en