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A generalization of the Allen–Cahn equation

Autor
Miranville, A.; Quintanilla, R.
Tipus d'activitat
Article en revista
Revista
IMA Journal of Applied Mathematics
Data de publicació
2015-04-01
Volum
80
Número
2
Pàgina inicial
410
Pàgina final
430
DOI
https://doi.org/10.1093/imamat/hxt044 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/27478 Obrir en finestra nova
URL
http://imamat.oxfordjournals.org/content/early/2013/11/15/imamat.hxt044 Obrir en finestra nova
Resum
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...
Citació
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.
Paraules clau
Allen–Cahn equation, Willmore regularization, dissipativity, global attractor, spatial behaviour, well-posedness
Grup de recerca
GRAA - Grup de Recerca en Anàlisi Aplicada

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