Periodic damping gives polynomial energy decay

Abstract

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 u decays at a rate (1 + t)−1/2. This is proved via a periodic observability estimate on R.

Locations

• Mathematical Research Letters - View
• arXiv (Cornell University) - View - PDF