Blow-up problem for semilinear heat equation with nonlinear nonlocal boundary condition

In this paper, we consider a semilinear parabolic equation with nonlinear nonlocal boundary condition and nonnegative initial datum. We prove some global existence results. Criteria on this problem which determine whether the solutions blow up in finite time for large or for all nontrivial initial data are also given. Moreover, we show that under certain conditions blow-up occurs only on the boundary.