Optimal control problems governed by some semilinear parabolic equations

Ryu, Sang-Uk

doi:10.1016/j.na.2003.09.013

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Cited by 16 publications

(10 citation statements)

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“…Yong and Zheng [43] considered the Cahn-Hilliard equation in a bounded domain with smooth boundary. Based on the energy estimates and the compact method, Ryu and Yagi [44,45] With = − , the optimal control problem for (7) we intend to investigate is…”

Section: Introductionmentioning

confidence: 99%

Optimal Control of a Viscous Shallow Water Equation

Zhang

Zhou

2013

Advances in Mathematical Physics

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Section: Introductionmentioning

confidence: 99%

Optimal Control of a Viscous Shallow Water Equation

Zhang

Zhou

2013

Advances in Mathematical Physics

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“…In [17], Yong and Zheng considered the feedback stabilization and optimal control of the Cahn-Hilliard equation in a bounded domain with smooth boundary. In the papers wrote by Ryu and Yagi [13,14], the optimal control problems of Keller-Segel equations and adsorbate-induced phase transition model were considered. Their techniques are based on the energy estimates and the compact method.…”

Section: Introductionmentioning

confidence: 99%

Optimal control for a higher-order nonlinear parabolic equation describing crystal surface growth

Duan

Zhao

2018

NAMC

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In this paper, we shall study the optimal control of the initial-boundary value problem of a higher-order nonlinear parabolic equation describing crystal surface growth. The existence and uniqueness of weak solutions to the problem are given. According to the variational method, optimal control theories and distributed parameter system control theories, we can deduce that the norm of the solution is related to the control item and initial value in the special Hilbert space. The optimal control of the problem is given, the existence of optimal solution is proved and the optimality system is established.

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“…In 1991, Yong and Zheng [11] studied the feedback stabilization and optimal control of the Cahn-Hilliard equation in a bounded domain with smooth boundary. In papers written by Ryu and Yagi [12,13], the optimal control problems of Keller-Segel equations and adsorbate-induced phase transition model were considered. Their techniques are based on the energy estimates and the compact method.…”

Section: Introductionmentioning

confidence: 99%