Convergence of the one-dimensional Cahn-Hilliard equation

2012/02/08 by Giovanni Bellettini, Lorenzo Bertini, Bellettini, Giovanni +5
Computer Science · Materials Science · Mathematics · #35K25 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.1202.1735

openalex publication_date 2012/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Cahn-Hilliard equation in one space dimension with scaling a small parameter εand a non-convex potential W. In the limit \espilon → 0, under the assumption that the initial data are energetically well-prepared, we show the convergence to a Stefan problem. The proof is based on variational methods and exploits the gradient flow structure of the Cahn-Hilliard equation.

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