In this talk, we shall discuss quantitative analysis of asymptotic behaviors of (possibly sign-changing) solutions to the Cauchy-Dirichlet problem for the fast diffusion equation posed on bounded domains with Sobolev subcritical exponents. More precisely, rates of convergence to non-degenerate asymptotic profiles will be revealed via an energy method. A sharp rate of convergence to positive asymptotic profiles was recently discussed by Bonforte and Figalli (2021, CPAM) based on an entropy method. An alternative proof for their result will also be provided.

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