Convergence of the Allen--Cahn Equation with a Nonlinear Robin Boundary Condition to Mean Curvature Flow with Contact Angle Close to 90°

DOI10.1137/21M1424925zbMath1485.35020arXiv2105.08434OpenAlexW4205235980MaRDI QIDQ5020860

Maximilian Moser, Helmut Abels

Publication date: 7 January 2022

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2105.08434

zbMATH Keywords

mean curvature flowRobin boundary conditioncontact angleAllen-Cahn equationsharp interface limit

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61) Moving boundary problems for PDEs (35R37) Pattern formations in context of PDEs (35B36) Flows related to mean curvature (53E10)

Related Items (4)

Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence result ⋮ Convergence rates for the Allen-Cahn equation with boundary contact energy: the non-perturbative regime ⋮ The Sharp Interface Limit of a Navier–Stokes/Allen–Cahn System with Constant Mobility: Convergence Rates by a Relative Energy Approach ⋮ Sharp Interface Limit for a Navier–Stokes/Allen–Cahn System with Different Viscosities

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