A stochastic selection principle in case of fattening for curvature flow
A stochastic selection principle in case of fattening for curvature flow
复制标题
曲率流增肥时的随机选择原理
DOI：
10.1007/s005260100080
复制
发表时间：
2001
影响因子：
2.1
通讯作者：
M. Novaga
中科院分区：
文献类型：
--
作者：
N. Dirr;S. Luckhaus;M. Novaga
抽象的。考虑两个不相交的圆以平均曲率加上一个使它们以零速度接触的强迫项运动。已知在粘性意义上的广义解在接触之后不再是曲线（所谓的肥化现象）。我们表明，在添加一个小的随机强迫$\mid} W$，在限制$\mid\0$的措施选择两个不断变化的曲线，在De Giorgi的意义上的上限和下限的障碍。此外，我们展示了非零$\n $的部分结果。
Abstract. Consider two disjoint circles moving by mean curvature plus a forcing term which makes them touch with zero velocity. It is known that the generalized solution in the viscosity sense ceases to be a curve after the touching (the so-called fattening phenomenon). We show that after adding a small stochastic forcing $\epsilon {\rm d} W$, in the limit $\epsilon\to 0$ the measure selects two evolving curves, the upper and lower barrier in the sense of De Giorgi. Further we show partial results for nonzero $\epsilon$.