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A degenerate Cahn‐Hilliard model as constrained Wasserstein gradient flow
Author(s) -
Matthes Daniel,
Cances Clement,
Nabet Flore
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900158
Subject(s) - balanced flow , discretization , degenerate energy levels , cahn–hilliard equation , constraint (computer aided design) , flow (mathematics) , mathematics , metric (unit) , variational inequality , wasserstein metric , mathematical analysis , mathematical optimization , physics , partial differential equation , geometry , operations management , quantum mechanics , economics
Existence of solutions to a non‐local Cahn‐Hilliard model with degenerate mobility is considered. The PDE is written as a gradient flow with respect to the L 2 ‐Wasserstein metric for two components that are coupled by an incompressibility constraint. Approximating solutions are constructed by means of an implicit discretization in time and variational methods.