Special asymptotics  for a critical fast diffusion equation

Marek Fila; Hannes Stuke

doi:10.3934/dcdss.2014.7.725

Article Contents

2014, Volume 7, Issue 4: 725-735. Doi: 10.3934/dcdss.2014.7.725

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Special asymptotics for a critical fast diffusion equation

Marek Fila^1, and
Hannes Stuke^2,

1.
Department of Applied Mathematics and Statistics, Comenius University, 84248 Bratislava
2.
Institut für Mathematik, Freie Universität Berlin, 14195 Berlin

Received: September 2013

Revised: November 2013

Published: August 2014

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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.

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Mathematics Subject Classification: Primary: 35K65; Secondary: 35B40.

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