一维随机Allen-Cahn方程的扭结运动
Kink motion for the one-dimensional stochastic Allen-Cahn equation
摘要：
研究了一维随机Allen-Cahn方程及其质量守恒方程的扭结运动。使用一个确定性的慢流形，在尖锐的接口限制足够小的噪声强度，我们推导出一个明确的随机微分方程的接口，这是有效的，只要解决方案保持接近的流形的运动。在一个相关的时间尺度上，其中接口移动最多的最小允许的接口之间的距离，我们表明，扭结的行为近似像驾驶维纳过程投影到慢流形上，而在质量守恒的情况下，他们另外耦合通过质量约束。
英文摘要：
We study the kink motion for the one-dimensional stochastic Allen-Cahn equation and its mass conserving counterpart. Using a deterministic slow manifold, in the sharp interface limit for sufficiently small noise strength we derive an explicit stochastic differential equation for the motion of the interfaces, which is valid as long as the solution stays close to the manifold. On a relevant time-scale, where interfaces move at most by the minimal allowed distance between interfaces, we show that the kinks behave approximately like the driving Wiener-process projected onto the slow manifold, while in the mass-conserving case they are additionally coupled via the mass constraint.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
