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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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Publisher copy:
10.1137/21M1391249

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
More by this author
Institution:
University of Oxford
Department:
MATHEMATICAL INSTITUTE
Sub department:
Mathematical Institute
Role:
Author
ORCID:
0000-0002-8325-3809


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:
1540-3467
ISSN:
1540-3459


Language:
English
Keywords:
Pubs id:
1173961
Local pid:
pubs:1173961
Deposit date:
2021-04-28

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