Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature flow
DOI10.4171/AIHPC/109zbMATH Open1545.35002MaRDI QIDQ6586921
Alice Marveggio, Julian Fischer
Publication date: 13 August 2024
Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)
phase-field modelsAllen-Cahn equationrelative entropy methodsharp interface limitmultiphase mean curvature flow
Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Dynamics of phase boundaries in solids (74N20) Variational methods applied to PDEs (35A15) Quasilinear parabolic equations with mean curvature operator (35K93) Flows related to mean curvature (53E10)
Cites Work
- On the motion of a curve by its binormal curvature
- Global asymptotic limit of solutions of the Cahn-Hilliard equation
- Sharp interface limit for a Stokes/Allen-Cahn system
- The effect of a singular perturbation on nonconvex variational problems
- Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics
- Generation and propagation of interfaces for reaction-diffusion equations
- Scaling limits and regularity results for a class of Ginzburg-Landau systems
- On three-phase boundary motion and the singular limit of a vector-valued Ginzburg-Landau equation
- Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature
- Convergence of the Cahn-Hilliard equation to the Hele-Shaw model
- Phase-field approximation of the Willmore flow
- Nematic-isotropic phase transition in liquid crystals: a variational derivation of effective geometric motions
- Weak-strong uniqueness for the Navier-Stokes equation for two fluids with ninety degree contact angle and same viscosities
- Weak-strong uniqueness for the Navier-Stokes equation for two fluids with surface tension
- Convergence of the Allen-Cahn equation to the mean curvature flow with \(90^\circ\)-contact angle in 2D
- Convergence of the parabolic Ginzburg-Landau equation to motion by mean curvature
- Convergence rates for the Allen-Cahn equation with boundary contact energy: the non-perturbative regime
- Phase transitions and generalized motion by mean curvature
- Complex Ginzburg-Landau equations and dynamics of vortices, filaments, and codimension-2 submanifolds
- Convergence of the Allen‐Cahn Equation to Multiphase Mean Curvature Flow
- Geometrical Evolution of Developed Interfaces
- Convergence Rates of the Allen--Cahn Equation to Mean Curvature Flow: A Short Proof Based on Relative Entropies
- Weak-strong uniqueness for the mean curvature flow of double bubbles
- Evolution of networks with multiple junctions
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