Blow-up for a degenerate diffusion problem not in divergence form

We study the behaviour of solutions of the nonlinear diffusion equation in the half-line, R+ = (0, infinity), with a nonlinear boundary condition, {ut = uu(xx), (x,t) is an element of R+ x (0, T), -ux (0,t) = u(p)(0,t) t is an element of (0, T), u(x,0) = u(0)(x), x is an element of R+, with p > 0. We describe, in terms of p and the initial datum, when the solution is global in time and when it blows up in finite time. For blowing up solutions we find the blow-up rate and the blow-up set and we describe the asymptotic behaviour close to the blow-up time in terms of a self-similar profile. The stationary character of the support is proved both for global solutions and blowing-up solutions. Also we obtain results for the problem in a bounded interval.