Journal article
How do degenerate mobilities determine singularity formation in Cahn-Hilliard equations?
- Abstract:
- Cahn-Hilliard models are central for describing the evolution of interfaces in phase separation processes and free boundary problems. In general, they have non-constant and often degenerate mobilities. However, in the latter case, the spontaneous appearance of points of vanishing mobility and their impact on the solution are not well understood. In this paper we develop a singular perturbation theory to identify a range of degeneracies for which the solution of the Cahn-Hilliard equation forms a singularity in infinite time. This analysis forms the basis for a rigorous sharp interface theory and enables the systematic development of robust numerical methods for this family of model equations.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, 1.1MB, Terms of use)
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- Publisher copy:
- 10.1137/21M1391249
Authors
- Publisher:
- Society for Industrial and Applied Mathematics
- Journal:
- Multiscale Modeling and Simulation More from this journal
- Volume:
- 19
- Issue:
- 3
- Pages:
- 1143–1166
- Publication date:
- 2021-07-13
- Acceptance date:
- 2021-04-26
- DOI:
- EISSN:
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1540-3467
- ISSN:
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1540-3459
- Language:
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English
- Keywords:
- Pubs id:
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1173961
- Local pid:
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pubs:1173961
- Deposit date:
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2021-04-28
Terms of use
- Copyright holder:
- Society for Industrial and Applied Mathematics.
- Copyright date:
- 2021
- Rights statement:
- © 2021, Society for Industrial and Applied Mathematics.
- Notes:
- This is the accepted manuscript version of the article. The final version is available from Society for Industrial and Applied Mathematics at: https://doi.org/10.1137/21M1391249
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