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

Abstract

In this paper, we consider a semilinear heat 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) = integral(Omega) k (x, y, t)u(l) dy and nonnegative initial data where p > 0 and I > 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. (c) 2007 Elsevier Inc. All rights reserved.