Mass conserving Allen-Cahn equation and volume preserving mean curvature flow
From MaRDI portal
Publication:629821
DOI10.4171/IFB/244zbMath1219.35018arXiv0902.3625OpenAlexW3100254834MaRDI QIDQ629821
Danielle Hilhorst, Elisabeth Logak, Xinfu Chen
Publication date: 10 March 2011
Published in: Interfaces and Free Boundaries (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0902.3625
singular perturbationsmall parameterboundary value problemconvergence of solutionsAllen-Cahn equation
Singular perturbations in context of PDEs (35B25) Initial-boundary value problems for second-order parabolic equations (35K20) Semilinear parabolic equations (35K58) Integro-partial differential equations (35R09)
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 ⋮ Consistent and conservative scheme for incompressible two-phase flows using the conservative Allen-Cahn model ⋮ A new interface capturing method for Allen-Cahn type equations based on a flow dynamic approach in Lagrangian coordinates. I: One-dimensional case ⋮ A stable and structure-preserving scheme for a non-local Allen-Cahn equation ⋮ On a model for phase separation on biological membranes and its relation to the Ohta–Kawasaki equation ⋮ Mass-conserving diffusion-based dynamics on graphs ⋮ Phase-field model of cell motility: traveling waves and sharp interface limit ⋮ On the mass-conserving Allen-Cahn approximation for incompressible binary fluids ⋮ Approximation of surface diffusion flow: A second-order variational Cahn–Hilliard model with degenerate mobilities ⋮ On an evolution equation in a cell motility model ⋮ Sharp interface limit in a phase field model of cell motility ⋮ The existence of a weak solution to volume preserving mean curvature flow in higher dimensions ⋮ A multiphase Cahn–Hilliard system with mobilities and the numerical simulation of dewetting ⋮ Arbitrarily high‐order accurate and energy‐stable schemes for solving the conservative Allen–Cahn equation ⋮ Numerical simulation for the conserved Allen-Cahn phase field model of two-phase incompressible flows by an efficient dimension splitting method ⋮ A regularized model for wetting/dewetting problems: positivity and asymptotic analysis ⋮ Sharp Interface Limit for a Navier–Stokes/Allen–Cahn System with Different Viscosities ⋮ Remarks on sharp interface limit for an incompressible Navier-Stokes and Allen-Cahn coupled system ⋮ Phase-field modeling and effective simulation of non-isothermal reactive transport ⋮ A Conservative Phase-Field Model for Reactive Transport ⋮ Novel mass-conserving Allen-Cahn equation for the boundedness of an order parameter ⋮ Generation of Interface for Solutions of the Mass Conserved Allen--Cahn Equation ⋮ Front propagation in the shadow wave-pinning model ⋮ Metastable dynamics for a hyperbolic variant of the mass conserving Allen-Cahn equation in one space dimension ⋮ A stochastically perturbed mean curvature flow by colored noise ⋮ Sharp interface limit for stochastically perturbed mass conserving Allen-Cahn equation ⋮ Sharp Interface Limits for Diffuse Interface Models for Two-Phase Flows of Viscous Incompressible Fluids ⋮ A two-scale iterative scheme for a phase-field model for precipitation and dissolution in porous media ⋮ Sharp interface limit of a Stokes/Cahn-Hilliard system. I: Convergence result ⋮ Second order linear thermodynamically consistent approximations to nonlocal phase field porous media models ⋮ High-order and mass conservative methods for the conservative Allen-Cahn equation ⋮ Well-posedness of a semi-discrete Navier-Stokes/Allen-Cahn model ⋮ A novel decoupled second-order time marching scheme for the two-phase incompressible Navier-Stokes/Darcy coupled nonlocal Allen-Cahn model ⋮ Numerical approximations of the Navier-Stokes equation coupled with volume-conserved multi-phase-field vesicles system: fully-decoupled, linear, unconditionally energy stable and second-order time-accurate numerical scheme ⋮ Sharp interface limit of a Stokes/Cahn-Hilliard system. II: Approximate solutions ⋮ The effective dynamics of the volume preserving mean curvature flow ⋮ Sharp interface limit for a Stokes/Allen-Cahn system ⋮ Unconditionally maximum bound principle preserving linear schemes for the conservative Allen-Cahn equation with nonlocal constraint ⋮ Fast explicit operator splitting method and time-step adaptivity for fractional non-local Allen-Cahn model ⋮ Phase-field approximation of the Willmore flow ⋮ Explicit third-order unconditionally structure-preserving schemes for conservative Allen-Cahn equations ⋮ Numerical approximation of the conservative Allen–Cahn equation by operator splitting method ⋮ On a linearized Mullins-Sekerka/Stokes system for two-phase flows ⋮ A fully-discrete decoupled finite element method for the conserved Allen-Cahn type phase-field model of three-phase fluid flow system ⋮ A novel fully-decoupled, linear, and unconditionally energy-stable scheme of the conserved Allen-Cahn phase-field model of a two-phase incompressible flow system with variable density and viscosity ⋮ Decoupled finite element scheme of the variable-density and viscosity phase-field model of a two-phase incompressible fluid flow system using the volume-conserved Allen-Cahn dynamics ⋮ Fully discrete spectral-Galerkin scheme for a ternary Allen-Cahn type mass-conserved Nakazawa-Ohta phase-field model for triblock copolymers ⋮ 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° ⋮ Global solutions to the volume-preserving mean-curvature flow
