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Periodic damping gives polynomial energy decay
Let u solve the damped Klein–Gordon equation ( ∂ t − ∑ ∂ xj +m Id +γ(x)∂t ) u = 0 on R with m > 0 and γ ≥ 0 bounded below on a 2πZ-invariant open set by a positive constant. We show that the energy of the solution …