Analysis on singular behavior of interfaces by multiple interface dynamics

研究了用椭圆曲率方程求解晶体表面螺旋演化的水平集方法。提出了交错螺旋的水平集方程，并进行了数值检验。得到了一群螺旋随椭圆曲率方程演化的稳定性。通过一个或多个螺旋步骤对晶体表面的生长速率进行了数值估计和检验。得到了非活动对条件下水平集方程的平稳解。得到了水平集方程近似方程解的Lipschitz连续性的先验估计。利用热方程的无限传播特性，提出了一种数据分离的扩散方法。

A level set method for evolving spirals by an eikonal-curvature equation on a crystal surface is studied. A level set equation for interlaced spiral is proposed and examined numerically. The stability of a bunch of spirals evolving with an eikonal-curvature equation is obtained. Growth rate of the crystal surface by a single or multiple spiral steps are estimated and examined numerically. Stationary solution to the level set equation with the situation of an inactive pair is obtained. A priori estimate for Lipschitz continuity of solutions to an approximating equation of the level set equation is obtained. A diffusion method for data separation is proposed as an application of the infinite propagation property on the heat equation.