Periodic damping gives polynomial energy decay

2015/11/19 by Jared Wunsch, Wunsch, Jared · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1511.06144

7 pages; final version takes into account referee comments

arxiv created 2016/08/19 · arxiv updated 2016/08/22

Abstract

Let u solve the damped Klein--Gordon equation ( ∂_t²-∑ ∂_xj² +m Id +γ(x) ∂_t ) u=0 on ℝⁿ with m>0 and γ≥ 0 bounded below on a 2 πℤⁿ-invariant open set by a positive constant. We show that the energy of the solution u decays at a polynomial rate. This is proved via a periodic observability estimate on ℝⁿ.

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