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Asymptotic stability and energy decay rates for solutions of hyperbolic equations with boundary damping†

Published online by Cambridge University Press:  14 February 2012

John P. Quinn  and
David L. Russell
John P. Quinn
Affiliation:
Department of Mathematics, University of Toronto
David L. Russell
Affiliation:
Department of Mathematics and Mathematics Research Center, University of Wisconsin
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Synopsis

This report deals with the asymptotic behaviour of solutions of the wave equation in a domain Ω ⊆Rn. The boundary, Γof Ωft consists of two parts. One part reflects all energy while the other part absorbs energy to a degree. If the energy-absorbing part is non-empty we show that the energy tends to zero as t→∞. With stronger assumptions we are able to obtain decay rates for the energy. Certain relationships with controlability are discussed and used to advantage.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 77 , Issue 1-2 , 1977 , pp. 97 - 127
Copyright
Copyright © Royal Society of Edinburgh 1977

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