Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Control and stabilization for the dispersion generalized Benjamin
  equation on the circle   This paper is concerned with controllability and stabilization properties of
the dispersion generalized Benjamin equation on the periodic domain
$\mathbb{T}.$ First, by assuming the control input acts on all the domain, the
system is proved to be globally exactly controllable in the Sobolev space
$H^{s}_{p}(\mathbb{T}),$ with $s\geq 0.$ Second, by providing a locally-damped
term added to the equation as a feedback law, it is shown that the resulting
equation is globally well-posed and locally exponentially stabilizable in the
space $L^{2}_{p}(\mathbb{T}).$ The main ingredient to prove the global
well-posedness is the introduction of the dissipation-normalized Bourgain
spaces which allows one to gain smoothing properties simultaneously from the
dissipation and dispersion present in the equation. Finally, the local
exponential stabilizability result is accomplished taking into account the
decay of the associated semigroup combined with the fixed point argument.

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The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom