Convergence of the Allen--Cahn Equation with Neumann Boundary Conditions

DOI10.1137/140987808zbMath1330.35196arXiv1403.5624OpenAlexW3104533527MaRDI QIDQ5254871

Masashi Mizuno, Yoshihiro Tonegawa

Publication date: 10 June 2015

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

Full work available at URL: https://arxiv.org/abs/1403.5624

zbMATH Keywords

mean curvature flowsingular limitAllen-Cahn equationvarifoldNeumann boundaryenergy measuresBrakke's mean curvature flow

Mathematics Subject Classification ID

Related Items (24)

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 ⋮ Gradient estimates for mean curvature flow with Neumann boundary conditions ⋮ Convergence of solutions of some Allen-Cahn equations to Brakke's mean curvature flow ⋮ Convergence rates for the Allen-Cahn equation with boundary contact energy: the non-perturbative regime ⋮ The existence of a weak solution to volume preserving mean curvature flow in higher dimensions ⋮ The Sharp Interface Limit of a Navier–Stokes/Allen–Cahn System with Constant Mobility: Convergence Rates by a Relative Energy Approach ⋮ Convergence of the Allen-Cahn equation with a zero Neumann boundary condition on non-convex domains ⋮ Lagrange multiplier and singular limit of double obstacle problems for the Allen-Cahn equation with constraint ⋮ The deep minimizing movement scheme ⋮ Mean curvature flow and low energy solutions of the parabolic Allen-Cahn equation on the three-sphere ⋮ Sharp Interface Limit for a Navier–Stokes/Allen–Cahn System with Different Viscosities ⋮ Level set mean curvature flow with Neumann boundary conditions ⋮ Convergence of phase-field free energy and boundary force for molecular solvation ⋮ Unnamed Item ⋮ The fractional Allen-Cahn equation with the sextic potential ⋮ Convergence of solutions of the weighted Allen-Cahn equations to Brakke type flow ⋮ A singular perturbation limit of diffused interface energy with a fixed contact angle condition ⋮ Erratum to “Convergence of the Allen--Cahn Equation 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 to the mean curvature flow with \(90^\circ\)-contact angle in 2D ⋮ Convergence of the Allen--Cahn Equation with a Nonlinear Robin Boundary Condition to Mean Curvature Flow with Contact Angle Close to 90° ⋮ Rectifiability of the free boundary for varifolds ⋮ Ground states of semilinear elliptic problems with applications to the Allen-Cahn equation on the sphere

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