Convergence rates of the allen-cahn equation to mean curvature flow: A short proof based on relative entropies

Julian Fischer, Tim Laux, Theresa M. Simon

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

We give a short and self-contained proof for rates of convergence of the Allen-Cahn equation towards mean curvature flow, assuming that a classical (smooth) solution to the latter exists and starting from well-prepared initial data. Our approach is based on a relative entropy technique. In particular, it does not require a stability analysis for the linearized Allen-Cahn operator. As our analysis also does not rely on the comparison principle, we expect it to be applicable to more complex equations and systems.

Original languageEnglish (US)
Pages (from-to)6222-6233
Number of pages12
JournalSIAM Journal on Mathematical Analysis
Volume52
Issue number6
DOIs
StatePublished - Dec 15 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Allen-Cahn equation
  • Diffuse interface
  • Mean curvature flow
  • Reaction-diffusion equations
  • Relative entropy method

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