Electron. J. Diff. Equ., Vol. 2012 (2012), No. 127, pp. 1-13.

Optimal control problem for a sixth-order Cahn-Hilliard equation with nonlinear diffusion

Changchun Liu, Zhao Wang

Abstract:
In this article, we study the initial-boundary-value problem for a sixth-order Cahn-Hilliard type equation
$$\displaylines{ u_t=D^2\mu, \cr \mu=\gamma D^4u-a(u)D^2u-\frac{a'(u)}2|D u|^2+f(u)+ku_t, }$$
which describes the separation properties of oil-water mixtures, when a substance enforcing the mixing of the phases is added. The optimal control of the sixth order Cahn-Hilliard type equation under boundary condition is given and the existence of optimal solution to the sixth order Cahn-Hilliard type equation is proved.

Submitted March 1, 2012. Published August 14, 2012.
Math Subject Classifications: 49J20, 35K35, 35K55.
Key Words: Cahn-Hilliard equation; existence; optimal control; optimal solution.

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Changchun Liu
Department of Mathematics, Jilin University
Changchun 130012, China
email: liucc@jlu.edu.cn
Zhao Wang
Department of Mathematics, Jilin University
Changchun 130012, China
email: wangzhao2717@163.com

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