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2003 The Spectrum of the Damped Wave Operator for a Bounded Domain in { $\boldsymbol{R^2}$}
Mark Asch, Gilles Lebeau
Experiment. Math. 12(2): 227-241 (2003).

Abstract

The spectrum of the damped wave operator for a bounded domain in {$R^2$} is shown to be related to the asymptotic average of the damping function by the geodesic flow. This allows the calculation of an asymptotic expression for the distribution of the imaginary parts of the eigenvalues for a radially symmetric geometry. Numerical simulations confirm the theoretical model. In addition, we are able to exhibit the beautiful structure of the spectrum and the close links between the eigenfunctions, the rays of geometrical optics, and the geometry of the damping region. The MATLAB code used in this paper is provided.

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Mark Asch. Gilles Lebeau. "The Spectrum of the Damped Wave Operator for a Bounded Domain in { $\boldsymbol{R^2}$}." Experiment. Math. 12 (2) 227 - 241, 2003.

Information

Published: 2003
First available in Project Euclid: 31 October 2003

zbMATH: 1061.35064
MathSciNet: MR2016708

Subjects:
Primary: 35P20
Secondary: 35B37 , 49J20 , 49K20 , 93C20

Keywords: damped wave equation , non-self-adjoint operator , spectrum

Rights: Copyright © 2003 A K Peters, Ltd.

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Vol.12 • No. 2 • 2003
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