Fast diffusion equations: Matching large time asymptotics by relative entropy methods

A non self-similar change of coordinates provides improved matching asymptotics of the solutions of the fast diffusion equation for large times, compared to already known results, in the range for which Barenblatt solutions have a finite second moment. The method is based on relative entropy estimates and a time-dependent change of variables which is determined by second moments, and not by the scaling corre- sponding to the self-similar Barenblatt solutions, as it is usually done.The research that led to the present paper was partially supported by a grant of the group GNFM of INdAM.