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

Ning Duan | Zendy; Xiaopeng Zhao | Zendy

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

Author(s) -

Ning Duan,

Xiaopeng Zhao

Publication year - 2018

Publication title -

nonlinear analysis modelling and control

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.734

H-Index - 32

eISSN - 2335-8963

pISSN - 1392-5113

DOI - 10.15388/na.2018.2.7

Subject(s) - uniqueness , optimal control , mathematics , hilbert space , nonlinear system , norm (philosophy) , boundary value problem , surface (topology) , mathematical analysis , parabolic partial differential equation , mathematical optimization , partial differential equation , physics , geometry , quantum mechanics , political science , law

. 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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