Blow-up for degenerate nonlinear parabolic problem

In this paper, we deal with the existence, uniqueness, and finite time blow-up of the solution to the degenerate nonlinear parabolic problem: u(tau) = (xi(r)u(m)u(xi))/xi(r) +u(p) or 0 < xi < a, 0 < tau < Gamma, u (xi, 0) = u(0) (xi) for 0 <= xi <= a, and u (0, tau) = 0 = u (a, tau) for 0 < tau < Gamma, where u(0) (xi) is a positive function and u(0) (0) = 0 = u(0) (a). In addition, we prove that u exists globally if a is small through constructing a global-exist upper solution, and u(tau) blows up in a finite time.