Electron. J. Differential Equations, Vol. 2018 (2018), No. 131, pp. 1-13.

Optimal distributed control problem for the modified Swift-Hohenberg equations

Bing Sun

This article concerns the optimal distributed control for the modified Swift-Hohenberg equation. Using the Dubovitskii and Milyutin functional analytical approach, we prove the Pontryagin maximum principle of the controlled modified Swift-Hohenberg equation. A necessary optimality condition is established for the problem in fixed final time horizon case. Also we indicate how to utilize the obtained results.

Submitted May 21, 2018. Published June 27, 2018.
Math Subject Classifications: 35Q35, 49B22, 49K20.
Key Words: Maximum principle; optimal distributed control; necessary optimality condition; Swift-Hohenberg equation.

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Bing Sun
School of Mathematics and Statistics
Beijing Institute of Technology
Beijing 100081, China
email: sunamss@gmail.com

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