论文标题
界面的布朗在一个有两个线性吸引组件和白色噪声的系统中的界面波动
Brownian fluctuations of the interface in a system with two linear attracted components and white noises
论文作者
论文摘要
我们涉及对具有两个组件的系统中界面的长时间行为的分析。每个组件根据1-D Allen-Cahn方程而演变为Neumann边界条件，在间隔$ [-ε^{ - 1}，ε^{ - 1}] $的间隔$ [ - ε^{ - 1}]中，具有对称的双井潜力的扰动。这两个组件通过有吸引力的线性力相互相互作用。 Instantons被定义为无噪声的Allen-Cahn方程的固定解，它连接了两个纯相。我们证明，在时间$ t =ε^{ - 1} $，在限制$ε\ rightarrow 0 $中，当初始状态接近intsanton时，两个组件保持接近同一intsanton，其中心作为布朗尼运动移动。
We concern the analysis of the long time behavior of interfaces in systems with two components. Each component evolves according to 1-d Allen-Cahn equation with Neumann boundary conditions, perturbed by small space-time white noise and with symmetric double well potential in the interval $[-ε^{-1},ε^{-1}]$. The two components interact with each other by an attractive linear force. Instantons are defined as the stationary solution of the Allen-Cahn equation without noise which connects two pure phases. We prove that for time $t=ε^{-1}$, in the limit $ε\rightarrow 0$, when initial states are close to an instanton, two components stay close to the same instanton, whose center moves as a Brownian motion.
