Optimal Control Problem for a Sixth-order Cahn-hilliard Equation with Nonlinear Diffusion

Abstract

In this article, we study the initial-boundary-value problem for a sixth-order Cahn-Hilliard type equation ut = D μ, μ = γDu− a(u)Du− a′(u) 2 |Du| + f(u) + kut, 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.

Cite this paper

@inproceedings{Liu2012OptimalCP, title={Optimal Control Problem for a Sixth-order Cahn-hilliard Equation with Nonlinear Diffusion}, author={Changchun Liu and Zhao Wang}, year={2012} }