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

In this paper, we consider a semilinear heat equation ut = u + c(x, t)up for (x, t) ∈ Ω × (0,∞) with nonlinear and nonlocal boundary condition u|∂Ω×(0,∞) = Ω k(x, y, t)ul dy and nonnegative initial data where p >0 and l > 0. We prove global existence theorem for max(p, l) 1. Some criteria on this problem which determine whether the solutions blow up in a finite time for sufficiently large or for all nontrivial initial data or the solutions exist for all time with sufficiently small or with any initial data are also given. © 2007 Elsevier Inc. All rights reserved.