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February  2010, 27(1): 25-52. doi: 10.3934/dcds.2010.27.25

Nucleation in the one-dimensional stochastic Cahn-Hilliard model

Dirk Blömker 1, , Bernhard Gawron 2, and  Thomas Wanner 3,

1. 

Institut für Mathematik, Universität Augsburg, 86159 Augsburg, Germany
2. 

Institut für Mathematik, RWTH Aachen, 52062 Aachen, Germany
3. 

Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, United States

Received  July 2009 Revised  October 2009 Published  February 2010

Despite their misleading label, rare events in stochastic systems are central to many applied phenomena. In this paper, we concentrate on one such situation - phase separation through homogeneous nucleation in binary alloys as described by the stochastic partial differential equation model due to Cahn, Hilliard, and Cook. We show that in the limit of small noise intensity, nucleation can be explained by the stochastically driven exit from the domain of attraction of an asymptotically stable homogeneous equilibrium state for the associated deterministic model. Furthermore, we provide insight into the subsequent nucleation dynamics via the structure of the attractor of the model in the absence of noise.
Keywords: nucleation, stochastic partial differential equation, large deviations, domain exit, Cahn-Hilliard-Cook model, attractor structure..
Mathematics Subject Classification: Primary: 35K55, 60F10, 60H15; Secondary: 35B40, 35B41, 74N9.
Citation: Dirk Blömker, Bernhard Gawron, Thomas Wanner. Nucleation in the one-dimensional stochastic Cahn-Hilliard model. Discrete and Continuous Dynamical Systems, 2010, 27 (1) : 25-52. doi: 10.3934/dcds.2010.27.25
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