Bai, F. and Elliott, C. M. and Gardiner, A. and Spence, A. and Stuart, A. M. (1995) The viscous Cahn-Hilliard equation. I. Computations. Nonlinearity, 8 (2). pp. 131-160. ISSN 0951-7715. doi:10.1088/0951-7715/8/2/002. https://resolver.caltech.edu/CaltechAUTHORS:20170612-135245414
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Abstract
The viscous Cahn-Hilliard equation arises as a singular limit of the phase-field model of phase transitions. It contains both the Cahn-Hilliard and Allen-Cahn equations as particular limits. The equation is in gradient form and possesses a compact global attractor A, comprising heteroclinic orbits between equilibria. Two classes of computation are described. First heteroclinic orbits on the global attractor are computed; by using the viscous Cahn-Hilliard equation to perform a homotopy, these results show that the orbits, and hence the geometry of the attractors, are remarkably insensitive to whether the Allen-Cahn or Cahn-Hilliard equation is studied. Second, initial-value computations are described; these computations emphasize three differing mechanisms by which interfaces in the equation propagate for the case of very small penalization of interfacial energy. Furthermore, convergence to an appropriate free boundary problem is demonstrated numerically.
| Item Type: | Article | |||||||||
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| Additional Information: | © 1995 IOP Publishing Ltd and LMS Publishing Ltd. Received 16 November 1993, in final form 27 September 1994. Work supported by UK Science Engineering Research Council grants. Work supported by the Office of Naval Research and the National Science Foundation under contracts N00014-92-J-1876 and DMS-9201727 respectively | |||||||||
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| Issue or Number: | 2 | |||||||||
| Classification Code: | AMS classification scheme numbers: 35K35, 65N25, 65N35, 65M99 | |||||||||
| DOI: | 10.1088/0951-7715/8/2/002 | |||||||||
| Record Number: | CaltechAUTHORS:20170612-135245414 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170612-135245414 | |||||||||
| Official Citation: | F Bai et al 1995 Nonlinearity 8 131 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 78118 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Tony Diaz | |||||||||
| Deposited On: | 12 Jun 2017 21:12 | |||||||||
| Last Modified: | 15 Nov 2021 17:36 |
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