Motion of a droplet for the Stochastic mass conserving Allen-Cahn equation

Hdl Handle:
http://hdl.handle.net/10034/582725
Title:
Motion of a droplet for the Stochastic mass conserving Allen-Cahn equation
Authors:
Antonopoulou, Dimitra; Bates, Peter W.; Bloemker, Dirk; Karali, Georgia D.
Abstract:
We study the stochastic mass-conserving Allen-Cahn equation posed on a smoothly bounded domain of R2 with additive, spatially smooth, space-time noise. This equation describes the stochastic motion of a small almost semicircular droplet attached to domain's boundary and moving towards a point of locally maximum curvature. We apply It^o calculus to derive the stochastic dynamics of the center of the droplet by utilizing the approximately invariant manifold introduced by Alikakos, Chen and Fusco [2] for the deterministic problem. In the stochastic case depending on the scaling, the motion is driven by the change in the curvature of the boundary and the stochastic forcing. Moreover, under the assumption of a su ciently small noise strength, we establish stochastic stability of a neighborhood of the manifold of boundary droplet states in the L2- and H1-norms, which means that with overwhelming probability the solution stays close to the manifold for very long time-scales.
Affiliation:
University of Chester
Citation:
Antonopoulou, D., & Bates, P., & Bloemker, D., & Karali, G. (2016). Motion of a droplet for the Stochastic mass conserving Allen-Cahn equation. SIAM Journal on Mathematical Analysis, 48(1), 670-708. DOI: 10.1137/151005105
Publisher:
SIAM
Journal:
SIAM Journal on Mathematical Analysis
Publication Date:
16-Feb-2016
URI:
http://hdl.handle.net/10034/582725
Additional Links:
http://epubs.siam.org/doi/abs/10.1137/151005105
Type:
Article
Language:
en
ISSN:
1095-7154
Appears in Collections:
Mathematics

Full metadata record

DC FieldValue Language
dc.contributor.authorAntonopoulou, Dimitraen
dc.contributor.authorBates, Peter W.en
dc.contributor.authorBloemker, Dirken
dc.contributor.authorKarali, Georgia D.en
dc.date.accessioned2015-11-25T14:55:37Zen
dc.date.available2015-11-25T14:55:37Zen
dc.date.issued2016-02-16en
dc.identifier.citationAntonopoulou, D., & Bates, P., & Bloemker, D., & Karali, G. (2016). Motion of a droplet for the Stochastic mass conserving Allen-Cahn equation. SIAM Journal on Mathematical Analysis, 48(1), 670-708. DOI: 10.1137/151005105en
dc.identifier.issn1095-7154en
dc.identifier.urihttp://hdl.handle.net/10034/582725en
dc.description.abstractWe study the stochastic mass-conserving Allen-Cahn equation posed on a smoothly bounded domain of R2 with additive, spatially smooth, space-time noise. This equation describes the stochastic motion of a small almost semicircular droplet attached to domain's boundary and moving towards a point of locally maximum curvature. We apply It^o calculus to derive the stochastic dynamics of the center of the droplet by utilizing the approximately invariant manifold introduced by Alikakos, Chen and Fusco [2] for the deterministic problem. In the stochastic case depending on the scaling, the motion is driven by the change in the curvature of the boundary and the stochastic forcing. Moreover, under the assumption of a su ciently small noise strength, we establish stochastic stability of a neighborhood of the manifold of boundary droplet states in the L2- and H1-norms, which means that with overwhelming probability the solution stays close to the manifold for very long time-scales.en
dc.language.isoenen
dc.publisherSIAMen
dc.relation.urlhttp://epubs.siam.org/doi/abs/10.1137/151005105en
dc.subjectSPDEsen
dc.titleMotion of a droplet for the Stochastic mass conserving Allen-Cahn equationen
dc.typeArticleen
dc.contributor.departmentUniversity of Chesteren
dc.identifier.journalSIAM Journal on Mathematical Analysisen
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