Research on numerical tracking methods for moving boundary and mathematical analysis of interface motion

我们的研究主题是通过数学分析和数值计算来理解界面运动。我们的目标是发展数学分析技术和移动边界的数值跟踪方法。(1)晶体曲率流动一般理论的建立(2)运动边界跟踪方法的发展，特别是保物性方法的发展(3)负晶体生长模型的进一步研究(4)含时间隙Hele-Shaw流动的数值计算(5)Hele-Shaw盒中产生气泡的数值计算(6)基于非局部Allen-Cahn方程的各向异性保面积曲率流动的研究

Main theme of our research is to understand interface motion by means of mathematical analysis and numerical computation. Our aim was development of technique of mathematical analysis and numerical tracking method of moving boundary. The followings are research keywords which we studied in this research period.(1) Construction of general theory for crystalline curvature flows(2) Development of tracking method for moving boundary, especially for preserving property scheme(3) Advanced research for negative crystal growth model(4) Numerical computation for Hele-Shaw flow with time-dependent gap(5) Numerical computation for arising bubble in the Hele-Shaw cell(6) Research for anisotropic area-preserving curvature flow by means of nonlocal Allen-Cahn equation