Optimal Shape Problems and Traction Method(Theory,Mathematical Design)

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  • KAIZU Satoshi
    Dept. of Mathematics, Faculty of Education Ibaraki University
  • AZEGAMI Hideyuki
    Dept. of Complex Systems, Graduate School of Information Science, Nagoya University

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  • 最適形状問題と力法について(理論,数理設計,<特集>平成18年研究部会連合発表会)
  • 数理設計 最適形状問題と力法について
  • スウリ セッケイ サイテキ ケイジョウ モンダイ ト リキホウ ニ ツイテ

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Abstract

In shape optimization, in which partial differential equations are defined and the shape with minimum cost is searched, an admissible family of shapes are given as being compact in some topology. Then minimizing of shapes for a cost implies an optimal shape, which we desire. The traction method is a power way to construct minimizing sequence of shapes for a cost, which guarantees the smoothness of shapes of the sequence. A reason of why the smoothness of shape is guaranteed is given from the point of view of mathematics.

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