  In this paper, we consider a nonlocal parabolic equation associated with
initial and Dirichlet boundary conditions. Firstly, we discuss the vacuum
isolating behavior of solutions with the help of a family of potential wells.
Then we obtain a threshold of global existence and blow up for solutions with
critical initial energy. Furthermore, for those solutions satisfy $J(u_0)\leq
d$ and $I(u_0)\neq 0$, we show that global solutions decay to zero
exponentially as time tends to infinity and the norm of blow-up solutions
increase exponentially.
