境界値問題を制約条件とする領域最適化問題の必要条件

抄録

In this paper are discussed the domain (shape) optimization problems in which a boundary value problem is a main constraint The approach developed by one of the authors is applied to slightly extended problems This approach is also applied to a problem of fluid mechanical engineering, namely, the minimumdrag problem in low Reynolds number limit. The outline of the approach is as follows; the existence of the variation of the solution, corresponding to a domain variation, to the boundary value problem is to be shown; the variational equation which relates the variation of the solution to the domain variation is to be derived; a neccessary condition is, then, to be obtained for each problem with a subsidiary constraint by the well-known Lagrange multiplier rule and by introducing adjoint variables. The domain optimization method demonstrated in this paper can be applied to other problems similar to those treated here.