Fast diffusion to self-similarity: Complete spectrum, long-time asymptotics, and numerology
The paper deals with the fast diffusion equation in the supercritical regime. The complete spectrum of the linearized problem is found, thus giving the sharp rates of asymptotic convergence to the Barenblatt profile. This bound improves some results in the literature, and suggests the conjecture that the self-similar function in mind is always the slowest to converge. It is also suggested how the rate of convergence can be improved.
scientific article; zbMATH DE number 2155995
scientific article