We consider the Cahn-Hilliard equation in one space dimension with scaling parameter epsilon, i.e., u(t) = (W'(u) - epsilon(2)u(xx))(xx), where W is a nonconvex potential. In the limit epsilon down arrow 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.
Bellettini, G., Bertini, L., Mariani, M., Novaga, M. (2012). Convergence of the One-Dimensional Cahn--Hilliard Equation. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 44(5), 3458-3480 [10.1137/120865410].
Convergence of the One-Dimensional Cahn--Hilliard Equation
BELLETTINI, GIOVANNI;
2012-01-01
Abstract
We consider the Cahn-Hilliard equation in one space dimension with scaling parameter epsilon, i.e., u(t) = (W'(u) - epsilon(2)u(xx))(xx), where W is a nonconvex potential. In the limit epsilon down arrow 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.| File | Dimensione | Formato | |
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