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1998 New Zealand Mathematics Colloquium
July 6-9, 1998
Victoria University of Wellington
Wellington, New Zealand

Organizers
Peter Donelan, Chris Atkin, John Harper, Philip Rhodes-Robinson, Jim Neyland, Geoff Whittle, Steve White, Vladimir Pestov, Tom Crosby

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Boundary Feedback Stabilisation of the Wave Equation
by
Steve Taylor
University of Auckland
Coauthors: Walter Littman (University of Minnesota)

The wave equation
\frac\partial2 w\partialt2=c2 \Deltaw
is the simplest partial differential equation that models the elastic vibrations of structures and it shows up in many different situations. Consequently, it was one of the first partial differential equations to be analysed, during the 70's and 80's, for the purpose of controlling the vibrations of such structures. In this talk, we will consider the boundary feedback stabilisation (i.e. stabilisation using energy dissipation at the boundary) of the wave equation, and indicate the problems that arise if the elastic medium is slightly inhomogeneous. We show how such problems can be resolved for a system consisting of a wave equation in one space dimension, coupled with an ordinary differential equation for the motion of a point mass (such a system is called a hybrid system).

Date received: May 22, 1998

Copyright © 1998 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cabd-21.