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arXiv · 1309.6173

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

Marek Fila·John R. King·Michael Winkler
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Abstract

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 which yields a non--linear 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 ({\sc Bonforte et al}. in Arch Rat Mech Anal 196:631--680, 2010) and provides answers to some open problems.

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Marek Fila, John R. King, Michael Winkler. 2013-09-24. Rate of Convergence to Barenblatt Profiles for the Fast Diffusion Equation with a Critical Exponent. https://doi.org/10.1112/jlms%2Fjdu025

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