Blow-up problem for semilinear heat equation with absorption and a nonlocal boundary condition

In this paper we consider a semilinear parabolic equation u(t) =Delta u - c (x, t)u(p) for (x, t) is an element of Omega x (0, infinity) with nonlinear and nonlocal boundary condition u vertical bar(partial derivative Omega x (0, infinity)) = f(Omega) k(x, y, t)u(l)dy and nonnegative initial data where p > 0 and l > 0. 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. (c) 2011 Elsevier Ltd. All rights reserved.