Geodesic
Optimal control problem for a sixth-order Cahn-Hilliard equation with nonlinear diffusion
Electronic journal of differential equations, Tome 2012 (2012)
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.
Classification : 49J20, 35K35, 35K55
Keywords: Cahn-Hilliard equation, existence, optimal control, optimal solution 
@article{EJDE_2012__2012__a50,
     author = {Liu,  Changchun and Wang,  Zhao},
     title = {Optimal control problem for a sixth-order {Cahn-Hilliard} equation with nonlinear diffusion},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1252.49006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a50/}
}
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%F EJDE_2012__2012__a50
Liu,  Changchun; Wang,  Zhao. Optimal control problem for a sixth-order Cahn-Hilliard equation with nonlinear diffusion. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a50/