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We study the asymptotic behaviour near extinction of positive solutions of the Cauchy problem for the fast diffusion equation with a critical exponent. After a suitable rescaling that yields a nonlinear Fokker–Planck equation, we find a continuum of algebraic rates of convergence to a self‐similar profile. These rates depend explicitly on the spatial decay rates of initial data. This improves a previous result on slow convergence for the critical fast diffusion equation and provides answers to some open problems.

Rate of convergence to Barenblatt profiles for the fast diffusion equation with a critical exponent