Convergence of the Allen-Cahn equation with a zero Neumann boundary condition on non-convex domains

DOI10.1007/s00208-018-1720-xzbMath1421.35192arXiv1710.00526OpenAlexW2761918954WikidataQ129583281 ScholiaQ129583281MaRDI QIDQ2419964

Takashi Kagaya

Publication date: 4 June 2019

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.00526

zbMATH Keywords

Allen-Cahn equationsingular limit problemBrakke's mean curvature flow

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Initial-boundary value problems for second-order parabolic equations (35K20) Length, area, volume, other geometric measure theory (28A75) Variational methods for second-order elliptic equations (35J20)

Related Items

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, Level set mean curvature flow with Neumann boundary conditions, Asymptotic behavior of Allen-Cahn-type energies and Neumann eigenvalues via inner variations, Singular Neumann Boundary Problems for a Class of Fully Nonlinear Parabolic Equations in One Dimension, Convergence of the Allen--Cahn Equation with a Nonlinear Robin Boundary Condition to Mean Curvature Flow with Contact Angle Close to 90°

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