Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Control and Stabilization of the Korteweg-de Vries Equation on a
  Periodic Domain   This paper aims at completing an earlier work of Russell and Zhang to study
internal control problems for the distributed parameter system described by the
Korteweg-de Vries equation on a periodic domain T^1. In their article, Russell
and Zhang showed that the system is locally exactly controllable and locally
exponentially stabilizable when the control acts on an arbitrary nonempty
subdomain of T^1. In this paper, we show that the system is in fact globally
exactly controllable and globally exponentially stabilizable. The global
exponential stabilizability corresponding to a natural feedback law is first
established with the aid of certain properties of propagation of compactness
and propagation of regularity in Bourgain spaces for solutions of the
associated linear system. Then, using a different feedback law, the resulting
closed-loop system is shown to be locally exponentially stable with an
arbitrarily large decay rate. A time-varying feedback law is further designed
to ensure a global exponential stability with an arbitrary large decay rate.

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The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs