Blow-up and propagation of disturbances for fast diffusion equations

This paper is concerned with the Cauchy problem for the fast diffusion equation ut−Δum=αup1ut−Δum=αup1 in RNRN (N≥1N≥1), where m∈(0,1)m∈(0,1), p1>1p1>1 and α>0α>0. The initial condition u0u0 is assumed to be continuous, nonnegative and bounded. Using a technique of subsolutions, we set up sufficient conditions on the initial value u0u0 so that u(t,x)u(t,x) blows up in finite time, and we show how to get estimates on the profile of u(t,x)u(t,x) for small enough values of t>0t>0.