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Title:
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A generalization of the Allen–Cahn equation
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Author:
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Miranville, Alain; Quintanilla de Latorre, Ramón
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II; Universitat Politècnica de Catalunya. GRAA - Grup de Recerca en Anàlisi Aplicada |
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Abstract:
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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. |
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Abstract:
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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. |
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Abstract:
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Peer Reviewed |
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Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials
-Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
-Differential equations, Parabolic
-Differential equations, Partial
-Allen–Cahn equation
-Willmore regularization
-well-posedness
-dissipativity
-global attractor
-spatial behaviour
-Equacions diferencials parabòliques
-Equacions en derivades parcials
-Classificació AMS::35 Partial differential equations::35B Qualitative properties of solutions
-Classificació AMS::35 Partial differential equations::35K Parabolic equations and systems |
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Rights:
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Document type:
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Article - Submitted version
Article |
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