Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On stabilization and control for the critical Klein-Gordon equation on a
  3-D compact manifold   In this article, we study the internal stabilization and control of the
critical nonlinear Klein-Gordon equation on 3-D compact manifolds. Under a
geometric assumption slightly stronger than the classical geometric control
condition, we prove exponential decay for some solutions bounded in the energy
space but small in a lower norm. The proof combines profile decomposition and
microlocal arguments. This profile decomposition, analogous to the one of
Bahouri-G\'erard on $\R^3$, is performed by taking care of possible geometric
effects. It uses some results of S. Ibrahim on the behavior of concentrating
waves on manifolds.

31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph