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

Abstract

Abstract. We study the behaviour of solutions of the nonlinear diffusion equation in the half-line, R + = (0, ∞), with a nonlinear boundary condition,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.