The Gateau derivative of cost functions in the optimal shape problems and the existence of the shape derivatives of solutions of the Stokes problems
The Gateau derivative of cost functions in the optimal shape problems and the existence of the shape derivatives of solutions of the Stokes problems
复制标题
最优形状问题中成本函数的Gateau导数及Stokes问题解的形状导数的存在性
DOI：
10.14495/jsiaml.1.17
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
S. Kaizu
中科院分区：
文献类型：
--
作者：
S. Kaizu
在最优形状问题中，成本对形状的导数是重要的，因为它给出了从初始形状开始的较低成本的方向。费用的可微性强烈地依赖于力学问题、定常线性化流动问题、Stokes问题的解的形状导数。形状导数通常由相关的材料导数自动给出。在充分条件下证明了形差导数的收敛性。这些条件适用于Stokes问题中速度和压力的形状导数的存在性。
In optimal shape problems the derivatives of costs with respect to shapes are important, because it gives a direction of lower cost from an initial shape. The differentiability of costs strongly depends on shape derivatives of solutions of mechanical problems, stationary linearized flow problems, the Stokes problems. The shape derivatives are usually given automatically by the associated material derivatives. We show the convergence of shape difference quotients under sufficient conditions. These conditions are applied to the existence of the shape derivatives of the velocity and the pressure in the Stokes problems.