论文标题
在随机反应扩散方程中呈指数长时间尺度上行驶波的稳定性
Stability of Travelling Waves on Exponentially Long Timescales in Stochastic Reaction-Diffusion Equations
论文作者
论文摘要
在本文中，我们为一类由乘法噪声项强迫的反应扩散方程的行驶波的元稳定性。特别是，我们表明，在[仓鼠2017，仓鼠2020]中开发的相跟踪技术可以在相对于噪声强度时长期长的时间尺度维持。这是通过将通用链接原理与伯克霍尔德·戴维斯·冈迪（Burkholder-Davis-Gundy）不平等的温和版本相结合，以在关键规律性制度中为随机卷积建立对数超级界限。
In this paper we establish the meta-stability of travelling waves for a class of reaction-diffusion equations forced by a multiplicative noise term. In particular, we show that the phase-tracking technique developed in [hamster2017,hamster2020] can be maintained over timescales that are exponentially long with respect to the noise intensity. This is achieved by combining the generic chaining principle with a mild version of the Burkholder-Davis-Gundy inequality to establish logarithmic supremum bounds for stochastic convolutions in the critical regularity regime.
