Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic stability of a Korteweg-de Vries equation with a
  two-dimensional center manifold   Local asymptotic stability analysis is conducted for an
initial-boundary-value problem of a Korteweg-de Vries equation posed on a
finite interval $\left[0, 2\pi \sqrt{7/3}\right]$. The equation comes with a
Dirichlet boundary condition at the left end-point and both of the Dirichlet
and Neumann homogeneous boundary conditions at the right end-point. It is known
that the associated linearized equation around the origin is not asymptotically
stable. In this paper, the nonlinear Korteweg-de Vries equation is proved to be
locally asymptotically stable around the origin through the center manifold
method. In particular, the existence of a two-dimensional local center manifold
is presented, which is locally exponentially attractive. By analyzing the
Korteweg-de Vries equation restricted on the local center manifold, a
polynomial decay rate of the solution is obtained.

27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom