Study of crack propagation models and moving boundary problems

在本研究中，我们从数学和数值分析的角度研究了断裂力学中的几种裂纹扩展模型以及与之相关的各种运动边界问题。这是完全不同的现象，然而，两者都有几何上的困难和变分结构的重要性。我们利用反应扩散系统这一运动边界问题的有力工具，成功地提出了一个相场模型，并构造了一个具有变结构的多边形运动及其数值分析。

In this research, we studied several crack propagation models in fracture mechanics and related various moving boundary problems from viewpoints of mathematical and numerical analyses. These are completely different phenomena, however, both have geometrical difficulty and importance of variational structures. We succeeded in proposing a phase field model by means of reaction diffusion system, which is a powerful tool in moving boundary problems, and constructed a polygonal motion with variational structure and its numerical analysis.