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arXiv · 2203.06397

Brownian fluctuations of the interface in a system with two linear attracted components and white noises

Tran Hoa Phu
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Abstract

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.

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Tran Hoa Phu. 2022-03-22. Brownian fluctuations of the interface in a system with two linear attracted components and white noises. https://arxiv.org/abs/2203.06397

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