Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic behavior of Boussinesq system of KdV-KdV type   This work deals with the local rapid exponential stabilization for a
Boussinesq system of KdV-KdV type introduced by J. Bona, M. Chen and J.-C.
Saut. This is a model for the motion of small amplitude long waves on the
surface of an ideal fluid. Here, we will consider the Boussinesq system of
KdV-KdV type posed on a finite domain, with homogeneous Dirichlet--Neumann
boundary controls acting at the right end point of the interval. Our goal is to
build suitable integral transformations to get a feedback control law that
leads to the stabilization of the system. More precisely, we will prove that
the solution of the closed-loop system decays exponentially to zero in the
$L^2(0,L)$--norm and the decay rate can be tuned to be as large as desired if
the initial data is small enough.

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The categories of this paper are: chem-ph
1
The categories of this paper are: cs
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The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat