OPTIMAL CONTROL OF A SINGULAR DIFFUSION EQUATION WITH CONSTRAINT

Ohtsuka, Takeshi; Shirakawa, Ken; Yamazaki, Noriaki

Hokkaido University Preprint Series in Mathematics, 2007, 875

Permalink : https://hdl.handle.net/2115/69684

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アクセス権	metadata only access
URI	https://hdl.handle.net/2115/69684
タイトル	OPTIMAL CONTROL OF A SINGULAR DIFFUSION EQUATION WITH CONSTRAINT
著者	Ohtsuka, Takeshi ; Shirakawa, Ken ; Yamazaki, Noriaki
著者名 Ohtsuka, Takeshi
著者名 Shirakawa, Ken
著者名 Yamazaki, Noriaki
言語	英語
発行日	2007
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	875
抄録	In this paper, we consider an optimal control problem for a state problem of a one dimensional Allen-Cahn type equation, which is derived from a free energy including the total variation interfacial energy and the constraint by the indicator function. So, the state problem contains the singular diffusion coming from the total variation, and another singular term coming from the constraint. The main conclusions of this paper are concerned with the existence of an optimal control (optimal pair) and the necessary condition (optimality condition) of an optimal pair. Furthermore, the analytic methods, performed in this paper, will provide an effective approximating approach to the optimal pairs of our control problem.
資源タイプ	その他