标题： 局部相位跟踪与随机反应扩散系统中平面波的亚稳态 显示英文标题

标题： Local Phase Tracking and Metastability of Planar Waves in Stochastic Reaction-Diffusion Systems

摘要： 平面行波$\mathbb R^d,$在$ d\geq 2,$上被证明在具有乘性噪声的反应扩散方程系统中，在长时间尺度上以高概率得以持续存在，前提是该波在一维（$d=1$）中是轨道稳定的。 虽然需要一个全局相位跟踪机制来确定一维或圆柱域上随机扰动波的位置，但我们表明，在整个无界空间上的行波可以通过仅追踪局部偏差来控制。 特别是，由噪声能量微小增加或从系统中撤回的能量几乎完全耗散到横向方向，留下的是小范围的局部相位偏移。 所考虑的噪声过程在时间上是白噪声，在空间上是彩色噪声，可能是加权的，并且要么是平移不变的，要么是迹类的。 显示英文摘要

摘要： Planar travelling waves on $\mathbb R^d,$ with $ d\geq 2,$ are shown to persist in systems of reaction-diffusion equations with multiplicative noise on significantly long timescales with high probability, provided that the wave is orbitally stable in dimension one ($d=1$). While a global phase tracking mechanism is required to determine the location of the stochastically perturbed wave in one dimension, or on a cylindrical domain, we show that the travelling wave on the full unbounded space can be controlled by keeping track of local deviations only. In particular, the energy infinitesimally added to or withdrawn from the system by noise dissipates almost fully into the transverse direction, leaving behind small localised phase shifts. The noise process considered is white in time and coloured in space, possibly weighted, and either translation invariant or trace class.