Generalized motion by mean curvature with Neumann conditions and the Allen-Cahn model for phase transitions

DOI10.1007/BF02921677zbMath0827.35003WikidataQ60149155 ScholiaQ60149155MaRDI QIDQ1897238

Markos A. Katsoulakis, Fernando Reitich, Georgios T. Kossioris

Publication date: 29 November 1995

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

zbMATH Keywords

viscosity solutionphase transitionsNeumann problemAllen-Cahn modelmotion by mean curvaturesharp-interface model

Mathematics Subject Classification ID

Related Items (29)

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 ⋮ A second order operator splitting method for Allen-Cahn type equations with nonlinear source terms ⋮ A new interface capturing method for Allen-Cahn type equations based on a flow dynamic approach in Lagrangian coordinates. I: One-dimensional case ⋮ Interacting particle systems and generalized evolution of fronts ⋮ A stable and structure-preserving scheme for a non-local Allen-Cahn equation ⋮ Instability of stationary solutions for equations of curvature-driven motion of curves ⋮ Comparison of different time discretization schemes for solving the Allen-Cahn equation ⋮ Exponentially slow dynamics and interfaces intersecting the boundary ⋮ Energy Stable Discontinuous Galerkin Finite Element Method for the Allen–Cahn Equation ⋮ Minimizing movements for mean curvature flow of droplets with prescribed contact angle ⋮ An unconditionally stable hybrid numerical method for solving the Allen-Cahn equation ⋮ 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 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 ⋮ Sharp Interface Limit for a Navier–Stokes/Allen–Cahn System with Different Viscosities ⋮ On a dynamic boundary condition for singular degenerate parabolic equations in a half space ⋮ Triply periodic minimal surface using a modified Allen-Cahn equation ⋮ A fast time two-mesh algorithm for Allen-Cahn equation ⋮ High-order and mass conservative methods for the conservative Allen-Cahn equation ⋮ Motion by curvature by scaling nonlocal evolution equations ⋮ The free-boundary Brakke flow ⋮ The Toda system and clustering interfaces in the Allen-Cahn equation ⋮ Convergence of solutions of the weighted Allen-Cahn equations to Brakke type flow ⋮ An efficient and accurate numerical algorithm for the vector-valued Allen-Cahn equations ⋮ 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 Neumann Boundary Conditions ⋮ 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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