Existence and blow-up for a degenerate parabolic equation with nonlocal source

In this paper, we investigate the positive solution of nonlinear degenerate equation u(t) = u(p)(Deltau+au integral(Omega)u(q) dx) with Dirichlet boundary condition. Conditions on the existence of global and blow-up solution are given. Furthermore, it is proved that there exist two positive constants C-1, C-2 such that C-1(T* - t)(-1/(p+q)) less than or equal to max(xis an element of(Ω) over bar) u(x, t) less than or equal to C-2(T* - t)(-1/(p+q)). (C) 2002 Elsevier Science Ltd. All rights reserved.