Metastable solutions for the thin-interface limit of a phase-field model

DOI10.1016/J.NA.2005.02.021zbMath1224.35396OpenAlexW2016751114MaRDI QIDQ999630

Ángela Jiménez-Casas

Publication date: 4 February 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2005.02.021

zbMATH Keywords

phase-fieldmetastable solutionsthin-interface limit

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) Stability in context of PDEs (35B35) Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10) PDEs in connection with mechanics of deformable solids (35Q74)

Cites Work

• Phase field models and sharp interface limits: Some differences in subtle situations
• The gradient theory of phase transitions and the minimal interface criterion
• Slow-motion manifolds, dormant instability, and singular perturbations
• The Dynamics of a Conserved Phase Field System: Stefan-like, Hele-Shaw, and Cahn-Hilliard Models as Asymptotic Limits
• Invariant manifolds for metastable patterns in u_t = ε²u_xx—f(u)
• On the slowness of phase boundary motion in one space dimension
• Linear stability analysis and metastable solutions for a phase-field model
• Slow Motion in One-Dimensional Cahn–Morral Systems
• Metastable patterns in solutions of u_t = ϵ²u_xx − f(u)
• Quantitative phase-field modeling of dendritic growth in two and three dimensions

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