论文标题
具有通用初始基准的Allen-Cahn方程
The Allen-Cahn equation with generic initial datum
论文作者
论文摘要
我们将Allen-Cahn方程$ \ partial_tu-ΔU= u-u^3 $，迅速混合高斯磁场是初始条件。我们表明，规定初始条件的幅度不太大，方程生成的前部由Bargmann-Fock Gaussian场的Nodal组描述，然后根据平均曲率流量进化。
We consider the Allen-Cahn equation $\partial_t u- Δu=u-u^3$ with a rapidly mixing Gaussian field as initial condition. We show that provided that the amplitude of the initial condition is not too large, the equation generates fronts described by nodal sets of the Bargmann-Fock Gaussian field, which then evolve according to mean curvature flow.
