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Fast diffusion to self-similarity: Complete spectrum, long-time asymptotics, and numerology. (English) Zbl 1083.35074
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.

MSC:
35P20 Asymptotic distributions of eigenvalues in context of PDEs
47F05 General theory of partial differential operators
47A10 Spectrum, resolvent
76R50 Diffusion
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