Metastability of the Cahn-Hilliard equation in one space dimension

DOI10.1016/j.jde.2018.04.012OpenAlexW2964112706MaRDI QIDQ2109136

Sebastian Scholtes, Maria G. Westdickenberg

Publication date: 20 December 2022

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.10985

zbMATH Keywords

gradient flownonlinear PDEenergy methodscoarsening ratesdynamic metastability

Mathematics Subject Classification ID

Parabolic equations and parabolic systems (35Kxx) Qualitative properties of solutions to partial differential equations (35Bxx) Phase transformations in solids (74Nxx)

Related Items

Optimal relaxation of bump-like solutions of the one-dimensional Cahn–Hilliard equation ⋮ On the metastability of the \(1-d\) Allen-Cahn equation ⋮ Corrigendum to: ``Metastability of the Cahn-Hilliard equation in one space dimension ⋮ Weak and strong interaction of excitation kinks in scalar parabolic equations ⋮ Distinguishing between long-transient and asymptotic states in a biological aggregation model ⋮ Relaxation to a planar interface in the Mullins-Sekerka problem ⋮ A gradient flow approach to relaxation rates for the multi-dimensional Cahn-Hilliard Equation ⋮ Optimal $L^1$-type Relaxation Rates for the Cahn--Hilliard Equation on the Line

Cites Work

• Generation, propagation, and annihilation of metastable patterns
• Slow motion for the Cahn-Hilliard equation in one space dimension
• Metastable patterns for the Cahn-Hilliard equation. I
• Metastable patterns for the Cahn-Hilliard equation. II: Layer dynamics and slow invariant manifold
• Slow-motion manifolds, dormant instability, and singular perturbations
• Slow motion of gradient flows
• Numerical Studies of the Cahn-Hilliard Equation for Phase Separation
• On the slowness of phase boundary motion in one space dimension
• On the slow dynamics for the Cahn–Hilliard equation in one space dimension
• Slow Motion in One-Dimensional Cahn–Morral Systems
• Metastable patterns in solutions of u_t = ϵ²u_xx − f(u)
• Dynamics and Coarsening of Interfaces for the Viscous Cahn—Hilliard Equation in One Spatial Dimension
• Optimal $L^1$-type Relaxation Rates for the Cahn--Hilliard Equation on the Line
• Relaxation to Equilibrium in the One-Dimensional Cahn--Hilliard Equation