Rate of Convergence to Barenblatt Profiles for the Fast Diffusion Equation

Abstract

We study the asymptotic behaviour of positive solutions of the Cauchy problem for the fast diffusion equation near the extinction time. We find a continuum of rates of convergence to a self-similar profile. These rates depend explicitly on the spatial decay rates of initial data.

References in corpus (3)

• Asymptotics of the fast diffusion equation via entropy estimates
• Sharp rates of decay of solutions to the nonlinear fast diffusion equation via functional inequalities
• Special fast diffusion with slow asymptotics. Entropy method and flow on a Riemannian manifold

Cited by in corpus (1)

• Rate of Convergence to Barenblatt Profiles for the Fast Diffusion Equation with a Critical Exponent