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.
CONVERGENCE OF THE ONE-DIMENSIONAL CAHN-HILLIARD EQUATION / Giovanni, Bellettini; BERTINI MALGARINI, Lorenzo; Mariani, Mauro; Matteo, Novaga. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - STAMPA. - 44:5(2012), pp. 3458-3480. [10.1137/120865410]
CONVERGENCE OF THE ONE-DIMENSIONAL CAHN-HILLIARD EQUATION
BERTINI MALGARINI, Lorenzo;MARIANI, Mauro;
2012
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
