Optimal control of the convective Cahn–Hilliard equation

Abstract

This article studies the problem for optimal control of the convective Cahn–Hilliard equation in one-space dimension. The optimal control under boundary condition is given, the existence of optimal solution to the equation is proved and the optimality system is established.

Keywords:

• optimal control
• convective Cahn–Hilliard equation
• optimal solution
• optimality condition

AMS Subject Classifications::

• 49A22
• 49K20

Acknowledgements

The authors thank the referees for their valuable comments and suggestions about this article.