Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The influence of the coefficients of a system of coupled wave equations
  with fractional damping on its stabilization   In this work, we consider a system of two wave equations coupled by
velocities in one-dimensional space, with one boundary fractional damping.
First, we show that the system is strongly asymptotically stable if and only if
the coupling parameter b of the two equations is outside a discrete set of
exceptional real values. Next, we show that our system is not uniformly stable.
Hence, we look for a polynomial decay rate for smooth initial data. Using
frequency domain approach combining with multiplier method, we prove that the
energy decay rate is greatly influenced by the nature of the coupling parameter
b, the arithmetic property of the ratio of the wave propagation speeds a, the
order of the fractional damping. Indeed, under the equal speed propagation
condition, we establish an optimal polynomial energy decay rate. Furthermore,
when the wave propagate with different speeds, under some arithmetic conditions
on the ratio of the wave propagation speeds, we prove that the energy of our
system decays polynomially to zero.

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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph
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The categories of this paper are: physics