Local minimizers and slow motion for the mass preserving Allen–Cahn equation in higher dimensions

DOI10.1090/proc/13988zbMath1431.49015OpenAlexW2766923761MaRDI QIDQ5238098

Giovanni Leoni, Ryan W. Murray

Publication date: 28 October 2019

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/proc/13988

zbMATH Keywords

Cahn-Hilliard equationslow motionAllen-Cahn equationCahn-Hilliard functionalsecond-order \(\Gamma\)-convergence

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Second-order parabolic equations (35K10) Higher-order parabolic equations (35K25)

Related Items (1)

Sharp interface limit of a multi-phase transitions model under nonisothermal conditions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Minimality via second variation for a nonlocal isoperimetric problem
• Translation of J. D. van der Waals' ``The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density
• Second order asymptotic development for the anisotropic Cahn-Hilliard functional
• Slow motion for the nonlocal Allen-Cahn equation in \(n\) dimensions
• Structured phase transitions on a finite interval
• The effect of a singular perturbation on nonconvex variational problems
• Distance to \(C^k\) hypersurfaces
• On the connectivity of boundaries of sets minimizing perimeter subject to a volume constraint
• An introduction to \(\Gamma\)-convergence
• Boundary regularity for solutions of a partitioning problem
• The gradient theory of phase transitions and the minimal interface criterion
• Slow-motion manifolds, dormant instability, and singular perturbations
• Asymptotic development by \(\Gamma{}\)-convergence
• Slow motion of gradient flows
• The sharp quantitative isoperimetric inequality
• Minimality via second variation for microphase separation of diblock copolymer melts
• Sets of Finite Perimeter and Geometric Variational Problems
• On the structure of equilibrium phase transitions within the gradient theory of fluids
• On the slowness of phase boundary motion in one space dimension
• Weakly Differentiable Functions
• Slow dynamics for the cahn-hilliard equation in higher space dimension part i: spectral estimates^∗
• Slow Motion in One-Dimensional Cahn–Morral Systems
• Metastable patterns in solutions of u_t = ϵ²u_xx − f(u)
• Sobolev Spaces
• Second-order \(\Gamma\)-limit for the Cahn-Hilliard functional

This page was built for publication: Local minimizers and slow motion for the mass preserving Allen–Cahn equation in higher dimensions