Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 127, pp. 1-13.
Title: Optimal control problem for a sixth-order Cahn-Hilliard
equation with nonlinear diffusion
Authors: Changchun Liu (Jilin Univ., Changchun, China)
Zhao Wang (Jilin Univ., Changchun, China)
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.