Convergence of the one-dimensional Cahn-Hilliard equation

Details Convergence of the one-dimensional Cahn-Hilliard equation Convergence of the one-dimensional Cahn-Hilliard equation

2012-02-08

arxiv.org/abs/1202.1735v1

Mathematics

Analysis of PDEs

23 pages

Scientific paper

We consider the Cahn-Hilliard equation in one space dimension with scaling a small parameter \epsilon and a non-convex potential W. In the limit \espilon \to 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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