Optimal distributed control for a coupled phase-field system

Bosheng Chen; Huilai Li; Changchun Liu

doi:10.3934/dcdsb.2021110

Article Contents

2022, Volume 27, Issue 3: 1789-1825. Doi: 10.3934/dcdsb.2021110

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Optimal distributed control for a coupled phase-field system

Department of Mathematics, Jilin University, Changchun 130012, China

^* Corresponding author: Changchun Liu
^* Corresponding author: Changchun Liu

Received: October 31, 2020

Revised: January 31, 2021

Early access: April 2021

Published: March 2022

This work is supported by the Jilin Scientific and Technological Development Program

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Abstract

Our aim is to consider a distributed optimal control problem for a coupled phase-field system which was introduced by Cahn and Novick-Cohen. First, we establish that the existence of a weak solution, in particular, we also obtain that a strong solution is uniqueness. Then the existence of optimal controls is proved. Finally we derive that the control-to-state operator is Fréchet differentiable and the first-order necessary optimality conditions involving the adjoint system are discussed as well.

Keywords:

Optimal distributed control,
Coupled phase-field system,
First-order necessary optimality conditions.

Mathematics Subject Classification: Primary: 49J20, 49K20; Secondary: 35M30.

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References

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