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dc.contributor.authorAntonopoulou, Dimitra
dc.contributor.authorKarali, Georgia D.
dc.contributor.authorTzirakis, Konstantinos
dc.date.accessioned2021-08-16T15:19:08Z
dc.date.available2021-08-16T15:19:08Z
dc.date.issued2021-08-27
dc.identifierhttps://chesterrep.openrepository.com/bitstream/handle/10034/625604/arxivAKT.pdf?sequence=1
dc.identifier.citationAntonopoulou, D., Karali, G., & Tzirakis, K. (2021). Layer dynamics for the one dimensional ε-dependent Cahn–Hilliard/Allen–Cahn equation. Calculus of Variations and Partial Differential Equations, 60, 207. https://doi.org/10.1007/s00526-021-02085-4en_US
dc.identifier.issn0944-2669
dc.identifier.doi10.1007/s00526-021-02085-4
dc.identifier.urihttp://hdl.handle.net/10034/625604
dc.descriptionThe final publication is available at Springer via http://dx.doi.org/10.1007/s00526-021-02085-4en_US
dc.description.abstractWe study the dynamics of the one-dimensional ε-dependent Cahn-Hilliard / Allen-Cahn equation within a neighborhood of an equilibrium of N transition layers, that in general does not conserve mass. Two different settings are considered which differ in that, for the second, we impose a mass-conservation constraint in place of one of the zero-mass flux boundary conditions at x = 1. Motivated by the study of Carr and Pego on the layered metastable patterns of Allen-Cahn in [10], and by this of Bates and Xun in [5] for the Cahn-Hilliard equation, we implement an N-dimensional, and a mass-conservative N−1-dimensional manifold respectively; therein, a metastable state with N transition layers is approximated. We then determine, for both cases, the essential dynamics of the layers (ode systems with the equations of motion), expressed in terms of local coordinates relative to the manifold used. In particular, we estimate the spectrum of the linearized Cahn-Hilliard / Allen-Cahn operator, and specify wide families of ε-dependent weights δ(ε), µ(ε), acting at each part of the operator, for which the dynamics are stable and rest exponentially small in ε. Our analysis enlightens the role of mass conservation in the classification of the general mixed problem into two main categories where the solution has a profile close to Allen-Cahn, or, when the mass is conserved, close to the Cahn-Hilliard solution.en_US
dc.publisherSpringeren_US
dc.relation.urlhttps://www.springer.com/journal/526en_US
dc.relation.urlhttps://link.springer.com/article/10.1007/s00526-021-02085-4
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/en_US
dc.subjectCahn-Hilliarden_US
dc.subjectAllen-Cahn equationen_US
dc.titleLayer dynamics for the one dimensional ε-dependent Cahn–Hilliard/Allen–Cahn equationen_US
dc.typeArticleen_US
dc.identifier.eissn1432-0835en_US
dc.contributor.departmentUniversity of Chester; University of Crete; IACM/FORTHen_US
dc.identifier.journalCalculus of Variations and Partial Differential Equationsen_US
or.grant.openaccessYesen_US
rioxxterms.funderUnfundeden_US
rioxxterms.identifier.projectUnfundeden_US
rioxxterms.versionAMen_US
rioxxterms.licenseref.startdate2022-08-27
dcterms.dateAccepted2021-08-02
rioxxterms.publicationdate2021-08-27
dc.date.deposited2021-08-16en_US
dc.indentifier.issn0944-2669en_US


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