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dc.contributor.authorMiranville, Alain
dc.contributor.authorQuintanilla de Latorre, Ramón
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II
dc.date.accessioned2015-04-21T13:31:16Z
dc.date.available2016-05-02T00:31:36Z
dc.date.created2015-04-01
dc.date.issued2015-04-01
dc.identifier.citationMiranville, A.; Quintanilla, R. A generalization of the Allen–Cahn equation. "IMA Journal of Applied Mathematics", 01 Abril 2015, vol. 80, núm. 2, p. 410-430.
dc.identifier.issn0272-4960
dc.identifier.urihttp://hdl.handle.net/2117/27478
dc.descriptionThis is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The version of record: Miranville, A.; Quintanilla, R. A generalization of the Allen–Cahn equation. "IMA Journal of Applied Mathematics", 01 Abril 2015, vol. 80, núm. 2, p. 410-430 is available online at:http://imamat.oxfordjournals.org/content/80/2/410.
dc.description.abstractOur aim in this paper is to study generalizations of the Allen–Cahn equation based on a modification of the Ginzburg–Landau free energy proposed in S. Torabi et al. (2009, A new phase-field model for strongly anisotropic systems. Proc. R. Soc. A, 465, 1337–1359). In particular, the free energy contains an additional term called Willmore regularization. We prove the existence, uniqueness and regularity of solutions, as well as the existence of the global attractor. Furthermore, we study the convergence to the Allen–Cahn equation, when the Willmore regularization goes to zero. We finally study the spatial behaviour of solutions in a semi-infinite cylinder, assuming that such solutions exist.
dc.format.extent21 p.
dc.language.isoeng
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
dc.subject.lcshDifferential equations, Parabolic
dc.subject.lcshDifferential equations, Partial
dc.subject.otherAllen–Cahn equation
dc.subject.otherWillmore regularization
dc.subject.otherwell-posedness
dc.subject.otherdissipativity
dc.subject.otherglobal attractor
dc.subject.otherspatial behaviour
dc.titleA generalization of the Allen–Cahn equation
dc.typeArticle
dc.subject.lemacEquacions diferencials parabòliques
dc.subject.lemacEquacions en derivades parcials
dc.contributor.groupUniversitat Politècnica de Catalunya. GRAA - Grup de Recerca en Anàlisi Aplicada
dc.identifier.doi10.1093/imamat/hxt044
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::35 Partial differential equations::35B Qualitative properties of solutions
dc.subject.amsClassificació AMS::35 Partial differential equations::35K Parabolic equations and systems
dc.relation.publisherversionhttp://imamat.oxfordjournals.org/content/early/2013/11/15/imamat.hxt044
dc.rights.accessOpen Access
drac.iddocument15560209
dc.description.versionPostprint (author’s final draft)
upcommons.citation.authorMiranville, A.; Quintanilla, R.
upcommons.citation.publishedtrue
upcommons.citation.publicationNameIMA Journal of Applied Mathematics
upcommons.citation.volume80
upcommons.citation.number2
upcommons.citation.startingPage410
upcommons.citation.endingPage430


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