Analysis on singular behavior of interfaces by multiple interface dynamics

用水平集方法研究了在晶体表面上用圆柱曲率方程演化螺旋线的方法。提出了交错螺线的水平集方程，并进行了数值验证。得到了一簇螺旋线的稳定性，并证明了螺旋线的演化具有圆锥-曲率方程。对单步或多步螺旋生长的晶体表面生长速率进行了估算和数值检验。得到了水平集方程在非活动对的情况下的定常解。得到了水平集方程逼近方程解的Lipschitz连续性的先验估计。作为对热方程无限传播性质的应用，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.