ヤマザキ ノリアキ   Yamazaki Noriaki
  山崎 教昭
   所属   神奈川大学  工学部 数学教室
    神奈川大学大学院  工学研究科 工学専攻(応用物理学領域)
   職種   教授
言語種別 英語
発行・発表の年月 2012
形態種別 学術雑誌
査読 査読あり
標題 Optimal control problem for Allen-Cahn type equation associated with total variation energy
執筆形態 共著
掲載誌名 Discrete and Continuous Dynamical Systems, Series S
出版社・発行元 AIMS
巻・号・頁 5,pp.159-181
著者・共著者 T. Ohtsuka and K. Shirakawa
概要 In this paper we study an optimal control problem for a singular
di usion equation associated with total variation energy. The singular di usion
equation is derived as an Allen-Cahn type equation, and then the observing
optimal control problem corresponds to a temperature control problem in the
solid-liquid phase transition. We show the existence of an optimal control
for our singular di usion equation by applying the abstract theory. Next we
consider our optimal control problem from the view-point of numerical analysis.
In fact we consider the approximating problem of our equation, and we show
the relationship between the original control problem and its approximating
one. Moreover we show the necessary condition of an approximating optimal
pair, and give a numerical experiment of our approximating control problem.