Singular limit of an Allen–Cahn equation with nonlinear diffusion

Perla El Kettani, Tadahisa Funaki, Danielle Hilhorst, Hyunjoon Park, Sunder Sethuraman

Research output: Contribution to journalArticlepeer-review


We consider an Allen–Cahn equation with nonlinear diffusion, motivated by the study of the scaling limit of certain interacting particle systems. We investigate its singular limit and show the generation and propagation of an interface in the limit. The evolution of this limit interface is governed by mean curvature flow with a novel, homogenized speed in terms of a surface tension-mobility parameter emerging from the nonlinearity in our equation.

Original languageEnglish (US)
Pages (from-to)719-754
Number of pages36
JournalTunisian Journal of Mathematics
Issue number4
StatePublished - Jan 1 2022


  • Allen–Cahn equation
  • interface
  • mean curvature flow
  • nonlinear diffusion
  • singular limit
  • surface tension

ASJC Scopus subject areas

  • Mathematics(all)


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