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dc.contributor.authorAntonopoulou, Dimitra*
dc.contributor.authorFarazakis, Dimitris*
dc.contributor.authorKarali, Georgia D.*
dc.date.accessioned2018-05-29T14:00:25Z
dc.date.available2018-05-29T14:00:25Z
dc.date.issued2018-05-08
dc.identifier.citationAntonopoulou, D., Farazakis, D., & Karali, G. D. (2018). Malliavin Calculus for the stochastic Cahn- Hilliard/Allen-Cahn equation with unbounded noise diffusion. Journal of Differential Equations, 265(7), 3168-3211.en
dc.identifier.issn0022-0396
dc.identifier.doi10.1016/j.jde.2018.05.004
dc.identifier.urihttp://hdl.handle.net/10034/621162
dc.description.abstractThe stochastic partial di erential equation analyzed in this work, is motivated by a simplified mesoscopic physical model for phase separation. It describes pattern formation due to adsorption and desorption mechanisms involved in surface processes, in the presence of a stochastic driving force. This equation is a combination of Cahn-Hilliard and Allen-Cahn type operators with a multiplicative, white, space-time noise of unbounded di usion. We apply Malliavin calculus, in order to investigate the existence of a density for the stochastic solution u. In dimension one, according to the regularity result in [5], u admits continuous paths a.s. Using this property, and inspired by a method proposed in [8], we construct a modi ed approximating sequence for u, which properly treats the new second order Allen-Cahn operator. Under a localization argument, we prove that the Malliavin derivative of u exists locally, and that the law of u is absolutely continuous, establishing thus that a density exists.
dc.language.isoenen
dc.publisherElsevieren
dc.relation.urlhttps://www.sciencedirect.com/science/article/pii/S0022039618302699en
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/en
dc.subjectStochastic partial differential equationsen
dc.subjectReaction-diffusion equationsen
dc.subjectPhase transitionsen
dc.subjectMalliavin Calculusen
dc.titleMalliavin Calculus for the stochastic Cahn- Hilliard/Allen-Cahn equation with unbounded noise diffusionen
dc.typeArticleen
dc.contributor.departmentUniversity of Chester; Foundation for Research and Technology; University of Creteen
dc.identifier.journalJournal of Differential Equations
dc.internal.reviewer-noteReplace full text with one in emails before uploading. GMen
dc.date.accepted2018-05-02
or.grant.openaccessYesen
rioxxterms.funderUnfundeden
rioxxterms.identifier.projectUnfundeden
rioxxterms.versionAMen
rioxxterms.licenseref.startdate2019-05-08
refterms.dateFCD2019-07-15T09:55:35Z
refterms.versionFCDAM
refterms.dateFOA2019-05-08T00:00:00Z
html.description.abstractThe stochastic partial di erential equation analyzed in this work, is motivated by a simplified mesoscopic physical model for phase separation. It describes pattern formation due to adsorption and desorption mechanisms involved in surface processes, in the presence of a stochastic driving force. This equation is a combination of Cahn-Hilliard and Allen-Cahn type operators with a multiplicative, white, space-time noise of unbounded di usion. We apply Malliavin calculus, in order to investigate the existence of a density for the stochastic solution u. In dimension one, according to the regularity result in [5], u admits continuous paths a.s. Using this property, and inspired by a method proposed in [8], we construct a modi ed approximating sequence for u, which properly treats the new second order Allen-Cahn operator. Under a localization argument, we prove that the Malliavin derivative of u exists locally, and that the law of u is absolutely continuous, establishing thus that a density exists.


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