On the Cahn-Hilliard equation.

*(English)*Zbl 0624.35048This paper is concerned with the Cahn-Hilliard equation which arises in the study of phase separation in cooling of binary solutions such as alloys, glasses and polymer mixtures. The initial boundary value problem for the Cahn-Hilliard equation is studied. Global existence and finite time blow up results are obtained. Error bounds for the finite element Galerkin approximation are proved.

When the solution globally exists, the asymptotic behavior of solution and the multiplicity of stationary solutions have been considered by the second author [Appl. Anal. 23, 165-184 (1986; Zbl 0613.35042)].

When the solution globally exists, the asymptotic behavior of solution and the multiplicity of stationary solutions have been considered by the second author [Appl. Anal. 23, 165-184 (1986; Zbl 0613.35042)].

##### MSC:

35K60 | Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations |

35B40 | Asymptotic behavior of solutions to PDEs |

35A05 | General existence and uniqueness theorems (PDE) (MSC2000) |

35K35 | Initial-boundary value problems for higher-order parabolic equations |

35A35 | Theoretical approximation in context of PDEs |

65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |

##### Keywords:

Cahn-Hilliard equation; phase separation; cooling of binary solutions; initial boundary value problem; Global existence; finite time blow up; finite element; Galerkin approximation; multiplicity of stationary solutions##### Citations:

Zbl 0613.35042
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\textit{C. M. Elliott} and \textit{S. Zheng}, Arch. Ration. Mech. Anal. 96, 339--357 (1986; Zbl 0624.35048)

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##### References:

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