论文标题
对热绝缘问题的稳定性分析
Stability analysis on the thermal insulation problems
论文作者
论文摘要
基于域变化的观点，我们对来自热绝缘背景的两个形状优化问题进行稳定分析。新颖的是，我们不要求第二个变化与边界垂直。 For example, translation variation is not normal, but as one can see in our work, it not only plays a role in obtaining the necessary and sufficient condition for stability of ball shape in the first problem when heat source is radial, but also is essential in deriving the precise value of symmetry breaking threshold of insulation material in the second problem, which turns out to be related to isoperimetric constant and in turn implies that ball shapes are stable in two dimensions.
Based on the domain variational point of view, we carry on stability analysis on two shape optimization problems from thermal insulation background. The novelty is that, we do not require that the second variation is normal to the boundary. For example, translation variation is not normal, but as one can see in our work, it not only plays a role in obtaining the necessary and sufficient condition for stability of ball shape in the first problem when heat source is radial, but also is essential in deriving the precise value of symmetry breaking threshold of insulation material in the second problem, which turns out to be related to isoperimetric constant and in turn implies that ball shapes are stable in two dimensions.
