  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
$t\rightarrow +\infty$.
