Imperfect geometric control and overdamping for the damped wave equation
Abstract
We consider the damped wave equation on a manifold with imperfect geometric control. We show the sub-exponential energy decay estimate in Chr-NC-erratum is optimal in the case of one hyperbolic periodic geodesic. We show if the equation is overdamped, then the energy decays exponentially. Finally we show if the equation is overdamped but geometric control fails for one hyperbolic periodic geodesic, then nevertheless the energy decays exponentially.
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