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Dec 2003 EIGENFREQUENCIES AND EXPANSIONS FOR DAMPED WAVE EQUATIONS
MICHAEL HITRIK
Methods Appl. Anal. 10(4): 543-564 (Dec 2003).

Abstract

We study eigenfrequencies and propagator expansions for damped wave equations on compact manifolds. Under the assumption of geometric control, the propagator is shown to admit an expansion in terms of finitely many eigenmodes near the real axis, with an error term exponentially decaying in time. In the presence of a nondegenerate elliptic closed geodesic not meeting the support of the damping coefficient, we show that there exists a sequence of eigenfrequencies converging rapidly to the real axis. In the case of Zoll manifolds, we show that the propagator can be expanded in terms of the clusters of the eigenfrequencies in the entire spectral band.

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MICHAEL HITRIK. "EIGENFREQUENCIES AND EXPANSIONS FOR DAMPED WAVE EQUATIONS." Methods Appl. Anal. 10 (4) 543 - 564, Dec 2003.

Information

Published: Dec 2003
First available in Project Euclid: 20 August 2004

zbMATH: 1088.58510
MathSciNet: MR1843407

Rights: Copyright © 2003 International Press of Boston

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Vol.10 • No. 4 • Dec 2003
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