一些形状为optimization的流动
Some flows in shape optimization
摘要：
研究了与Bernoulli型形状最优化问题有关的几何流动。演化律是一个曲率项和一个Hele-Shaw型非局部项之和。我们引入广义集合解，其定义广泛地受到黏性解的启发。主要结果是广义解的包含保持原理。从而得到了解的存在性、唯一性和稳定性。讨论了该流动的渐近性质：证明了其解收敛于广义Bernoulli外自由边界问题。
英文摘要：
Geometric flows related to shape optimization problems of Bernoulli type are investigated. The evolution law is the sum of a curvature term and a nonlocal term of Hele-Shaw type. We introduce generalized set solutions, the definition of which is widely inspired by viscosity solutions. The main result is an inclusion preservation principle for generalized solutions. As a consequence, we obtain existence, uniqueness and stability of solutions. Asymptotic behavior for the flow is discussed: we prove that the solutions converge to a generalized Bernoulli exterior free boundary problem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
