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1995 Quasi-optimal error estimates for the mean curvature flow with a forcing term
G. Bellettini, M. Paolini
Differential Integral Equations 8(4): 735-752 (1995). DOI: 10.57262/die/1369055609


We study a singularly perturbed reaction-diffusion equation with a small parameter $\epsilon>0$. This problem is viewed as an approximation of the evolution of an interface by its mean curvature with a forcing term. We derive a quasi-optimal error estimate of order $\mathcal{O}(\epsilon^2| \rm{log}\, \epsilon|^2)$ for the interfaces, which is valid before the onset of singularities, by constructing suitable sub and super solutions. The proof relies on the behavior at infinity of functions appearing in the truncated asymptotic expansion, and by using a modified distance function combined with a vertical shift.


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G. Bellettini. M. Paolini. "Quasi-optimal error estimates for the mean curvature flow with a forcing term." Differential Integral Equations 8 (4) 735 - 752, 1995.


Published: 1995
First available in Project Euclid: 20 May 2013

zbMATH: 0820.49019
MathSciNet: MR1306590
Digital Object Identifier: 10.57262/die/1369055609

Primary: 35B25
Secondary: 35K57 , 58E12

Rights: Copyright © 1995 Khayyam Publishing, Inc.


Vol.8 • No. 4 • 1995
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