On the coupled Cahn-Hilliard equations.

*(English)*Zbl 0815.35041Summary: This paper is concerned with the coupled Cahn-Hilliard equations, which consists of a fourth order quasilinear parabolic equation and a second order quasilinear parabolic equation. The global existence and uniqueness of classical solutions is proved. Results about the asymptotic behavior and about the existence and multiplicity of solutions to the corresponding stationary problem, which is a nonlinear boundary value problem involving nonlocal term and constraints, are also obtained.

##### MSC:

35K55 | Nonlinear parabolic equations |

35B40 | Asymptotic behavior of solutions to PDEs |

35K45 | Initial value problems for second-order parabolic systems |

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\textit{W. Shen} and \textit{S. Zheng}, Commun. Partial Differ. Equations 18, No. 3--4, 701--727 (1993; Zbl 0815.35041)

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##### References:

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