论文标题
平均具有粗糙系数的随机PDE的慢速原理
Averaging principle for slow-fast systems of stochastic PDEs with rough coefficients
论文作者
论文摘要
在本文中，我们考虑了一类随机部分微分方程的缓慢快速系统，其中慢速方程中的非线性不是连续且无限的。我们首先提供确保存在Martingale解决方案的条件。然后，我们证明缓慢运动的定律很紧，其任何限制点都是适合平均方程式的Martingale解决方案。我们的结果适用于随机反应扩散方程的系统，在缓慢方程中的反应项仅连续并且具有多项式生长。
In this paper, we consider a class of slow-fast systems of stochastic partial differential equations where the nonlinearity in the slow equation is not continuous and unbounded. We first provide conditions that ensure the existence of a martingale solution. Then we prove that the laws of the slow motions are tight, and any of their limiting points is a martingale solution for a suitable averaged equation. Our results apply to systems of stochastic reaction-diffusion equations where the reaction term in the slow equation is only continuous and has polynomial growth.
