Optimal controls of multidimensional modified Swift–Hohenberg equation

Abstract

In this paper, we deal with the optimal control problem governed by multidimensional modified Swift–Hohenberg equation. After showing the relationship between the control problem and its approximation, we derive the optimality conditions for an optimal control of our original problem by using one of the approximate problems.

Keywords:

• optimal control
• modified Swift–Hohenberg equation
• optimality condition

2010 AMS Subject Classifications:

• 35K57
• 49J20
• 49J30

Acknowledgements

The authors also would like to thank to the referees for revising the manuscript and for many valuable comments that helped clarify this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.