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dc.contributor.authorAntonopoulou, Dimitra
dc.date.accessioned2023-01-03T15:01:03Z
dc.date.available2023-01-03T15:01:03Z
dc.date.issued2023-01-03
dc.identifierhttps://chesterrep.openrepository.com/bitstream/handle/10034/627406/Antonopoulou_St-C-H-higher-moments.pdf?sequence=1
dc.identifier.citationAntonopoulou, D. (2023). Higher moments for the Stochastic Cahn - Hilliard Equation with multiplicative Fourier noise. Nonlinearity, 36(2), 1053. https://doi.org/10.1088/1361-6544/acadc9en_US
dc.identifier.issn0951-7715
dc.identifier.urihttp://hdl.handle.net/10034/627406
dc.description‘This is the Accepted Manuscript version of an article accepted for publication in [Nonlinearity]. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at [https://doi.org/10.1088/1361-6544/acadc9].’en_US
dc.description.abstractWe consider in dimensions $d=1,2,3$ the $\eps$-dependent stochastic Cahn-Hilliard equation with a multiplicative and sufficiently regular in space infinite dimensional Fourier noise with strength of order $\mathcal{O}(\eps^\gamma)$, $\gamma>0$. The initial condition is non-layered and independent from $\eps$. Under general assumptions on the noise diffusion $\sigma$, we prove moment estimates in $H^1$ (and in $L^\infty$ when $d=1$). Higher $H^2$ regularity $p$-moment estimates are derived when $\sigma$ is bounded, yielding as well space H\"older and $L^\infty$ bounds for $d=2,3$, and path a.s. continuity in space. All appearing constants are expressed in terms of the small positive parameter $\eps$. As in the deterministic case, in $H^1$, $H^2$, the bounds admit a negative polynomial order in $\eps$. Finally, assuming layered initial data of initial energy uniformly bounded in $\eps$, as proposed by X.F. Chen in \cite{chenjdg}, we use our $H^1$ $2$d-moment estimate and prove the stochastic solution's convergence to $\pm 1$ as $\eps\rightarrow 0$ a.s., when the noise diffusion has a linear growth.en_US
dc.publisherIOP Publishingen_US
dc.relation.urlhttps://iopscience.iop.org/article/10.1088/1361-6544/acadc9en_US
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/en_US
dc.subjectStochastic Cahn-Hilliard equationen_US
dc.subjectIt\^o calculusen_US
dc.subjectMultiplicative infinite dimensional noiseen_US
dc.subjectHigher moment estimatesen_US
dc.titleHigher moments for the Stochastic Cahn - Hilliard Equation with multiplicative Fourier noiseen_US
dc.typeArticleen_US
dc.identifier.eissn1361-6544en_US
dc.contributor.departmentUniversity of Chesteren_US
dc.identifier.journalNonlinearityen_US
or.grant.openaccessYesen_US
rioxxterms.funderNon fundeden_US
rioxxterms.identifier.projectNon fundeden_US
rioxxterms.versionAMen_US
rioxxterms.versionofrecord10.1088/1361-6544/acadc9en_US
rioxxterms.licenseref.startdate2024-01-03
dcterms.dateAccepted2022-12-21
rioxxterms.publicationdate2023-01-03
dc.date.deposited2023-01-03en_US
dc.indentifier.issn0951-7715en_US


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