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On the vibrations of a square membrane

Published online by Cambridge University Press:  14 November 2011

V. Komornik
V. Komornik
Affiliation:
Mathematical Institute, Eötvös Loránd University, Múzeum krt. 6-8, Budapest, H-1088, Hungary
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Synopsis

We establish that if Ω is an open square and if P is an arbitrary point of Ω, then the solutions of the wave equation with Dirichlet boundary condition utt − Δu = 0 in R × Ω, u = 0 on R × Γ can remain strictly positive during an arbitrarily large time. In fact stronger results are proved, considering several points of Ω simultaneously and prescribing different, more general, behaviour of the solution at these points.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 111 , Issue 1-2 , 1989 , pp. 13 - 20
Copyright
Copyright © Royal Society of Edinburgh 1989

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