Convergence of the One-Dimensional Cahn-Hilliard Equation
نویسندگان
چکیده
We consider the Cahn-Hilliard equation in one space dimension with scaling parameter ε, i.e. ut = (W ′(u) − εuxx)xx, where W is a nonconvex potential. In the limit ε ↓ 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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ورودعنوان ژورنال:
- SIAM J. Math. Analysis
دوره 44 شماره
صفحات -
تاریخ انتشار 2012