Erratum

Inwon C. Kim

doi:10.3934/dcds.2011.30.375

Article Contents

2011, Volume 30, Issue 1: 375-377. Doi: 10.3934/dcds.2011.30.375

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Erratum

Inwon C. Kim^1,

1.
UCLA Mathematics Department, Box 951555, Los Angeles, CA 90095-1555

Received: November 2010

Published: January 2011

Abstract / Introduction Related Papers Cited by

Abstract

The earlier paper [2] contains a lower bound of the solution in terms of its $L^1$ norm, which is incorrect. In this note we explain the mistake and present a correction to it under the restriction that the permeability constant $m$ satisfies $1< m <2$. As a consequence, the quantitative estimates on the convergence rate (Main Theorem (c) and Theorem 3.6 in [2] ) only hold for $1<\m<2$. For $\m\geq 2$ a partial convergence rate is obtained.

Keywords:

Mathematics Subject Classification: 35B51, 35B40, 35K55.

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References

[1]	E. DiBenedetto, U. Gianazza and V. Vespri, Harnack estimates for quasi-linear degenerate parabolic differential equations, Acta Math., 200 (2008), 181-209.doi: 10.1007/s11511-008-0026-3.
[2]	Inwon C. Kim and Helen K. Lei, Degenerate diffusion with a drift potential: A viscosity solution approach, Dis. and Con. Dyn. Sys., 27 (2010), 767-786.doi: 10.3934/dcds.2010.27.767.
[3]	J. L. Vazquez, "The Porous Medium Equation: Mathematical Theory," Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, Oxford, 2007.