Existence and nonexistence of global solutions of some nonlocal degenerate parabolic equations

This paper investigates the global existence and nonexistence of positive solutions of the nonlinear degenerate parabolic equation u(t) = f(u)(Deltau + a integral(Omega) u dx) with a homogeneous Dirichlet boundary condition. It is proved that there exists no global positive solution if and only if integral(infinity) 1/(sf (s)) ds < infinity and integral(Omega) rho(x) dx > 1/a, where rho(x) is the unique positive solution of the linear elliptic problem -Deltarho(x) 1, x is an element of n; rho(x) = 0, x is an element of thetaOmega. (C) 2003 Elsevier Science Ltd. All rights reserved.