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Singular limit of an
Allen–Cahn equation with nonlinear diffusion
Perla El Kettani, Tadahisa Funaki, Danielle Hilhorst, Hyunjoon Park and Sunder Sethuraman |
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Vol. 4 (2022), No. 4, 719–754
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Abstract |
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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. |
Keywords
Allen–Cahn equation, mean curvature flow, singular limit,
nonlinear diffusion, interface, surface tension
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Mathematical Subject Classification
Primary: 35B25, 35B40, 35B51, 35K57, 35K59
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Milestones
Received: 26 December 2021
Revised: 22 June 2022
Accepted: 14 July 2022
Published: 15 January 2023
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Authors |
| Perla El Kettani | |
| University of Toulon Toulon France |
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| Tadahisa Funaki | |
| Graduate School of Mathematical
Sciences Department of Mathematics University of Tokyo Tokyo Japan |
Department of Mathematics Waseda University Tokyo Japan |
| Danielle Hilhorst | |
| CNRS and Laboratoire de
Mathématiques Paris-Saclay University Orsay France |
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| Hyunjoon Park | |
| Department of Mathematical
Sciences Korean Advanced Institute of Science and Technology Daejeon South Korea |
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| Sunder Sethuraman | |
| Department of Mathematics University of Arizona Tucson, AZ United States |
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