Singular limit of an Allen–Cahn equation with nonlinear diffusion

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

doi:10.2140/tunis.2022.4.719

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 journal › Article › peer-review

1 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	719-754
Number of pages	36
Journal	Tunisian Journal of Mathematics
Volume	4
Issue number	4
DOIs	https://doi.org/10.2140/tunis.2022.4.719
State	Published - Jan 1 2022
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

General Mathematics

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10.2140/tunis.2022.4.719

Cite this

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AU - Hilhorst, Danielle

AU - Park, Hyunjoon

AU - Sethuraman, Sunder

PY - 2022/1/1

Y1 - 2022/1/1

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AB - 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.

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KW - mean curvature flow

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KW - singular limit

KW - surface tension

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Singular limit of an Allen–Cahn equation with nonlinear diffusion

Abstract

Keywords

ASJC Scopus subject areas

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