The blow-up profile for a fast diffusion equation with a nonlinear boundary condition

Abstract

We study positive solutions of a fast diffusion equation in the half-line with a nonlinear boundary condition, (ut=(umxx (x, t)∈'R+×(0, T), (-um)x(0, t) = up(0, t)t∈(0, T), u(x, 0)=u0(x) x∈R+, where 0 0 are parameters. We describe in terms of p and m when all solutions exist globally in time, when all solutions blow up in a finite time, and when there are both blowing up and global solutions. For blowing up solutions we find the blow-up rate and the blow-up set and we describe the asymptotic behavior close to the blow-up time T in terms of a self-similar profile. © 2003 Rocky Mountain Mathematics Consortium.