# American Institute of Mathematical Sciences

July  2011, 10(4): 1129-1147. doi: 10.3934/cpaa.2011.10.1129

## A continuum of extinction rates for the fast diffusion equation

 1 Department of Applied Mathematics and Statistics, Comenius University, 842 48 Bratislava 2 Departamento de Matemáticas, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid 3 Fakultät für Mathematik, Universität Duisburg-Essen, 45117 Essen, Germany

Received  September 2010 Revised  November 2011 Published  April 2011

We find a continuum of extinction rates for solutions $u(y,\tau)\ge 0$ of the fast diffusion equation $u_\tau=\Delta u^m$ in a subrange of exponents $m\in (0,1)$. The equation is posed in $R^n$ for times up to the extinction time $T>0$. The rates take the form $\|u(\cdot,\tau)\|_\infty$ ~ $(T-\tau)^\theta$ for a whole interval of $\theta>0$. These extinction rates depend explicitly on the spatial decay rates of initial data.
Citation: Marek Fila, Juan-Luis Vázquez, Michael Winkler. A continuum of extinction rates for the fast diffusion equation. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1129-1147. doi: 10.3934/cpaa.2011.10.1129
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