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April  2011, 30(1): 375-377. doi: 10.3934/dcds.2011.30.375

Erratum

Inwon C. Kim 1,

1. 

UCLA Mathematics Department, Box 951555, Los Angeles, CA 90095-1555, United States

Received  November 2010 Published  February 2011

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: degenerate diffusion, asymptotic convergence., Viscosity solutions.
Mathematics Subject Classification: 35B51, 35B40, 35K5.
Citation: Inwon C. Kim. Erratum. Discrete & Continuous Dynamical Systems, 2011, 30 (1) : 375-377. doi: 10.3934/dcds.2011.30.375
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.  Google Scholar

[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.  Google Scholar

[3]

J. L. Vazquez, "The Porous Medium Equation: Mathematical Theory," Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, Oxford, 2007. Google Scholar

show all references

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.  Google Scholar

[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.  Google Scholar

[3]

J. L. Vazquez, "The Porous Medium Equation: Mathematical Theory," Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, Oxford, 2007. Google Scholar

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