Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global dynamics of a parabolic type equation arising from the curvature
  flow   This paper studies a type of degenerate parabolic problem with nonlocal term
\begin{equation*}
  \begin{cases}
  u_t=u^p(u_{xx}+u-\bar{u}) & 0<t<T_{{\max}},\ 0<x<a,
  u_x(0,t)=u_x(a,t)=0 & 0<t<T_{{\max}},
  u(x,0)=u_0(x) & 0<x<a,
  \end{cases} \end{equation*} where $p>1$, $a>0$. In this paper, the
classification of the finite-time blowup/global existence phenomena based on
the associated energy functional and explicit expression of all nonnegative
steady states are demonstrated. Moreover, we combine the applications of
Lojasiewicz-Simon inequality and energy estimates to derive that any bounded
solution with positive initial data converges to some steady state as
$t\rightarrow +\infty$.

1
The categories of this paper are: cs
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat