Quasi-optimal error estimates for the mean curvature flow with a forcing term

Maurizio Paolini, Giovanni Bellettini, G. Bellettini, P. L. Lions

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

34 Citazioni (Scopus)

Abstract

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 $\O(\epsilon^2|\log\epsilon|^2)$ for the interfaces, which is valid before the onset of singularities, by constructing suitable sub and super solutions. The proof relies on the behaviour at infinity of functions appearing in the truncated asymptotic expansion, and by using a modified distance function combined with a vertical shift.
Lingua originaleEnglish
pagine (da-a)735-752
Numero di pagine18
RivistaDifferential and Integral Equations
Stato di pubblicazionePubblicato - 1995

Keywords

  • Allen-Cahn equation
  • mean curvature flow

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