On a smooth bounded Euclidean domain,  Sobolev-subcritical fast diffusion with vanishing boundary trace leads to finite-time extinction, with a vanishing profile selected by the initial datum. In rescaled variables, we quantify the rate of convergence to this profile uniformly in relative error,  showing the rate is either exponentially fast (with a rate constant predicted by the spectral gap) or algebraically slow (which is only possible in the presence of zero modes). In the first case, we identify the leading order asymptotics. Our results improve various results in the literature,  while shortening their proofs. Joint work with Beomjun Choi and Robert J. McCann.

Zoom meeting: Link