Discrete and Continuous Dynamical Systems - Series S (DCDS-S)

Special asymptotics for a critical fast diffusion equation

Pages: 725 - 735, Volume 7, Issue 4, August 2014      doi:10.3934/dcdss.2014.7.725

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Marek Fila - Department of Applied Mathematics and Statistics, Comenius University, 84248 Bratislava, Slovak Republic (email)
Hannes Stuke - Institut für Mathematik, Freie Universität Berlin, 14195 Berlin, Germany (email)

Abstract: We find a continuum of extinction rates of solutions of the Cauchy problem for the fast diffusion equation $u_\tau=\nabla\cdot(u^{m-1}\,\nabla u)$ with $m=m_*:=(n-4)/(n-2)$, here $n>2$ is the space-dimension. The extinction rates depend explicitly on the spatial decay rates of initial data and contain a logarithmic term.

Keywords:  Fast diffusion, extinction in finite time, nonlinear Fokker-Planck equation, grow-up.
Mathematics Subject Classification:  Primary: 35K65; Secondary: 35B40.

Received: September 2013;      Revised: November 2013;      Available Online: February 2014.