Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp Polynomial Decay for Waves Damped from the Boundary in Cylindrical
  Waveguides   We study the decay of global energy for the wave equation with H\"older
continuous damping placed on the $C^{1,1}$-boundary of compact and non-compact
waveguides with star-shaped cross-sections. We show there is sharp
$t^{-1/2}$-decay when the damping is uniformly bounded from below on the
cylindrical wall of product cylinders where the Geometric Control Condition is
violated. On non-product cylinders, we also show that there is $t^{-1/3}$-decay
when the damping is uniformly bounded from below on the cylindrical wall.

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The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
1
The categories of this paper are: cs
16
The categories of this paper are: stat