Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Imperfect geometric control and overdamping for the damped wave equation   We consider the damped wave equation on a manifold with imperfect geometric
control. We show the sub-exponential energy decay estimate in
\cite{Chr-NC-erratum} is optimal in the case of one hyperbolic periodic
geodesic. We show if the equation is overdamped, then the energy decays
exponentially. Finally we show if the equation is overdamped but geometric
control fails for one hyperbolic periodic geodesic, then nevertheless the
energy decays exponentially.

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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
3
The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: quant-ph