Let u solve the damped Klein.Gordon equation ( ∂Ý t-σ +∂Ý xj + mId+(x)∂t u = 0 on Rn with m > 0 and Á . 0 bounded below on a 2ÎZn-invariant open set by a positive constant. We show that the energy of a solution decays at a polynomial rate. This is proved via a periodic observability estimate on Rn.
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