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The Cahn-Hilliard equation. (English) Zbl 1185.35001
Dafermos, C.M.(ed.) et al., Handbook of differential equations: Evolutionary equations. Vol. IV. Amsterdam: Elsevier/North-Holland (ISBN 978-0-444-53034-9/hbk). Handbook of Differential Equations, 201-228 (2008).
The paper is devoted to analysis of the Cahn-Hilliard equation. This equation has been seen to contain many of the dominant paradigms for phase separation. First, the author outlines the physical features and phenomena which may be described by this equation. Then, the author sums up results for the constant-quadratic polynomial case, i.e., for the constant mobility Cahn-Hilliard equation. A major part in the paper is assigned to issues of the existence, uniqueness, and regularity of global solutions. Problems of linear stability, long time behavior and limiting motions are also discussed. Some rigorous results on upper bounds for coarsening are given.
For the entire collection see [Zbl 1173.35002].

MSC:
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35B25 Singular perturbations in context of PDEs
35K35 Initial-boundary value problems for higher-order parabolic equations
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