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The sharp interface limit for the stochastic Cahn-Hilliard Equation
Antonopoulou, Dimitra Bloemker, Dirk Karali, Georgia D.
Antonopoulou, Dimitra
Bloemker, Dirk
Karali, Georgia D.
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2018-02-19
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Abstract
We study the two and three dimensional stochastic Cahn-Hilliard equation in the sharp
interface limit, where the positive parameter \eps tends to zero, which measures the width of transition
layers generated during phase separation. We also couple the noise strength to this parameter.
Using formal asymptotic expansions, we identify the limit. In the right scaling we indicate that the
solutions of stochastic Cahn-Hilliard converge to a solution of a Hele-Shaw problem with stochastic
forcing. In the case when the noise is sufficiently small, we rigorously prove that the limit is a
deterministic Hele-Shaw problem. Finally, we discuss which estimates are necessary in order to
extend the rigorous result to larger noise strength.
Citation
Antonopoulou, D., Bloemker, D. & Karali, G. (2018). The sharp interface limit for the stochastic Cahn-Hilliard Equation. Annales de l'Institut Henri Poincaré Probabilités et Statistiques, 54(1), 280-298. http://doi.org/10.1214/16-AIHP804
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IMS Journals
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Annales de l'Institut Henri Poincaré Probabilités et Statistiques
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Article
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en
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0246-0203