Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Damped wave equations on compact hyperbolic surfaces   We prove exponential decay of energy for solutions of the damped wave
equation on compact hyperbolic surfaces with regular initial data as long as
the damping is nontrivial. The proof is based on a similar strategy as in
Dyatlov-Jin and in particular, uses the fractal uncertainty principle proved in
Bourgain-Dyatlov.

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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph