@article{c9bf3786a7a14048904ee212646872bc,
title = "Singular limit of an Allen–Cahn equation with nonlinear diffusion",
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.",
keywords = "Allen–Cahn equation, interface, mean curvature flow, nonlinear diffusion, singular limit, surface tension",
author = "{El Kettani}, Perla and Tadahisa Funaki and Danielle Hilhorst and Hyunjoon Park and Sunder Sethuraman",
note = "Funding Information: The authors are grateful to the professors Henri Berestycki and Fran{\c c}ois Hamel for useful discussions. P. El Kettani, D. Hilhorst and H. J. Park thank IRN ReaDiNet as well as the French-Korean project STAR. T. Funaki was supported in part by JSPS KAKENHI, Grant-in-Aid for Scientific Researches (A) 18H03672 and (S) 16H06338, and also thanks IRN ReaDiNet. S. Sethuraman was supported by grant ARO W911NF-181-0311, a Simons Foundation Sabbatical grant, and by a JSPS Fellowship, and thanks Waseda University for the kind hospitality during a sabbatical visit. Publisher Copyright: {\textcopyright} 2022 Mathematical Sciences Publishers.",
year = "2022",
month = jan,
day = "1",
doi = "10.2140/tunis.2022.4.719",
language = "English (US)",
volume = "4",
pages = "719--754",
journal = "Tunisian Journal of Mathematics",
issn = "2576-7658",
publisher = "Mathematical Science Publishers",
number = "4",
}