Energy Decay for the Damped Wave Equation Under a Pressure Condition |
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Authors: | Emmanuel Schenck |
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Institution: | 1. Institut de Physique Théorique, CEA Saclay, 91191, Gif-sur-Yvette, France
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Abstract: | We establish the presence of a spectral gap near the real axis for the damped wave equation on a manifold with negative curvature.
This result holds under a dynamical condition expressed by the negativity of a topological pressure with respect to the geodesic
flow. As an application, we show an exponential decay of the energy for all initial data sufficiently regular. This decay
is governed by the imaginary part of a finite number of eigenvalues close to the real axis. |
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Keywords: | |
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