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A generalization of the Allen–Cahn equation
dc.contributor.author | Miranville, Alain |
dc.contributor.author | Quintanilla de Latorre, Ramón |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II |
dc.date.accessioned | 2015-04-21T13:31:16Z |
dc.date.available | 2016-05-02T00:31:36Z |
dc.date.created | 2015-04-01 |
dc.date.issued | 2015-04-01 |
dc.identifier.citation | 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. |
dc.identifier.issn | 0272-4960 |
dc.identifier.uri | http://hdl.handle.net/2117/27478 |
dc.description | This 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.abstract | Our 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.extent | 21 p. |
dc.language.iso | eng |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals |
dc.subject.lcsh | Differential equations, Parabolic |
dc.subject.lcsh | Differential equations, Partial |
dc.subject.other | Allen–Cahn equation |
dc.subject.other | Willmore regularization |
dc.subject.other | well-posedness |
dc.subject.other | dissipativity |
dc.subject.other | global attractor |
dc.subject.other | spatial behaviour |
dc.title | A generalization of the Allen–Cahn equation |
dc.type | Article |
dc.subject.lemac | Equacions diferencials parabòliques |
dc.subject.lemac | Equacions en derivades parcials |
dc.contributor.group | Universitat Politècnica de Catalunya. GRAA - Grup de Recerca en Anàlisi Aplicada |
dc.identifier.doi | 10.1093/imamat/hxt044 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::35 Partial differential equations::35B Qualitative properties of solutions |
dc.subject.ams | Classificació AMS::35 Partial differential equations::35K Parabolic equations and systems |
dc.relation.publisherversion | http://imamat.oxfordjournals.org/content/early/2013/11/15/imamat.hxt044 |
dc.rights.access | Open Access |
local.identifier.drac | 15560209 |
dc.description.version | Postprint (author’s final draft) |
local.citation.author | Miranville, A.; Quintanilla, R. |
local.citation.publicationName | IMA Journal of Applied Mathematics |
local.citation.volume | 80 |
local.citation.number | 2 |
local.citation.startingPage | 410 |
local.citation.endingPage | 430 |
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