Dynamics near extinction time of a singular diffusion equation

We will show that if u is the solution of the equation , in is an even function on and is monotone decreasing in on , , where is a monotone increasing function satisfying with being given by and , then the rescaled function , will converge uniformly on every compact subset of to as where . Received: 25 May 2000 / Revised version: 26 October 2001 / Published online: 28 February 2002