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The viscous Cahn-Hilliard equation. I. Computations

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. 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
Related URLs:
URLURL TypeDescription
https://doi.org/10.1088/0951-7715/8/2/002DOIArticle
http://iopscience.iop.org/article/10.1088/0951-7715/8/2/002/metaPublisherArticle
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
Funders:
Funding AgencyGrant Number
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
Office of Naval Research (ONR)N00014-92-J-1876
NSFDMS-9201727
Other Numbering System:
Other Numbering System NameOther Numbering System ID
Andrew StuartJ29
Issue or Number:2
Classification Code:AMS classification scheme numbers: 35K35, 65N25, 65N35, 65M99
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:03 Oct 2019 18:05

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