Decays rates for Kelvin-Voigt damped wave equations II: the geometric control condition

Abstract

We study in this article decay rates for Kelvin-Voigt damped wave equations under a geometric control condition. We prove that when the damping coefficient is sufficiently smooth ($C^1$ vanishing nicely) we show that exponential decay follows from geometric control conditions (see~\cite{BuCh, Te12} for similar results under stronger assumptions on the damping function).

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• A N-dimensional elastic\viscoelastic transmission problem with Kelvin-Voigt damping and non smooth coefficient at the interface