The sharp interface limit for the stochastic Cahn-Hilliard Equation

Hdl Handle:
http://hdl.handle.net/10034/620253
Title:
The sharp interface limit for the stochastic Cahn-Hilliard Equation
Authors:
Antonopoulou, Dimitra; Bloemker, Dirk; Karali, Georgia D.
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.
Affiliation:
Universiy of Chester
Citation:
Antonopoulou, D., Bloemker, D. & Karali, G. (2017-forthcoming). The sharp interface limit for the stochastic Cahn-Hilliard Equation. Annales de l'Institut Henri Poincaré Probabilités et Statistiques.
Publisher:
IMS Journals
Journal:
Annales de l'Institut Henri Poincaré Probabilités et Statistiques
Publication Date:
2017
URI:
http://hdl.handle.net/10034/620253
Additional Links:
http://imstat.org/aihp/default.htm
Type:
Article
Language:
en
ISSN:
0246-0203
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorAntonopoulou, Dimitraen
dc.contributor.authorBloemker, Dirken
dc.contributor.authorKarali, Georgia D.en
dc.date.accessioned2016-11-15T11:12:42Z-
dc.date.available2016-11-15T11:12:42Z-
dc.date.issued2017-
dc.identifier.citationAntonopoulou, D., Bloemker, D. & Karali, G. (2017-forthcoming). The sharp interface limit for the stochastic Cahn-Hilliard Equation. Annales de l'Institut Henri Poincaré Probabilités et Statistiques.en
dc.identifier.issn0246-0203-
dc.identifier.urihttp://hdl.handle.net/10034/620253-
dc.description.abstractWe 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.en
dc.language.isoenen
dc.publisherIMS Journalsen
dc.relation.urlhttp://imstat.org/aihp/default.htmen
dc.subjectSPDEsen
dc.titleThe sharp interface limit for the stochastic Cahn-Hilliard Equationen
dc.typeArticleen
dc.contributor.departmentUniversiy of Chesteren
dc.identifier.journalAnnales de l'Institut Henri Poincaré Probabilités et Statistiquesen
dc.date.accepted2016-10-26-
or.grant.openaccessYesen
rioxxterms.funderunfundeden
rioxxterms.identifier.projectunfundeden
rioxxterms.versionAMen
rioxxterms.licenseref.startdate2016-12-31-
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