Calculus of Variations and Geometric Measure Theory
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G. Bellettini - L. Bertini - M. Mariani - M. Novaga

Convergence of the one-dimensional Cahn-Hilliard Equation

created by novaga on 07 Feb 2012
modified on 07 Jan 2016


Published Paper

Inserted: 7 feb 2012
Last Updated: 7 jan 2016

Journal: SIAM J. on Math. Anal.
Volume: 44
Number: 5
Pages: 3458-3480
Year: 2012


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 $\epsilon\to 0$, 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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