Blow-up and propagation of disturbances for fast diffusion equations

This paper is concerned with the Cauchy problem for the fast diffusion equation u(t) - Delta u(m) = alpha u(p1) in R-N (N >= 1), where m epsilon (0, 1), p(1) > 1 and alpha > 0. The initial condition u(0) is assumed to be continuous, nonnegative and bounded. Using a technique of subsolutions, we set up sufficient conditions on the initial value u(0) so that u(t, x) blows up in finite time, and we show how to get estimates on the profile of u(t, x) for small enough values of t > 0. (C) 2007 Elsevier Ltd. All rights reserved.