论文标题
多尺度随机汉堡方程的最佳收敛顺序
Optimal convergence order for multi-scale stochastic Burgers equation
论文作者
论文摘要
在本文中，我们研究了多尺度一维随机汉堡方程的强和弱收敛速率。基于Galerkin近似，Kolmogorov方程和泊松方程的技术，我们分别以1/2和1的最佳顺序获得了缓慢的组分，分别以弱收敛到相应平均方程的溶液。系统中高度非线性的术语给我们带来了巨大的困难，我们开发了克服这些困难的新技术。据我们所知，这项工作似乎是第一个结果，即具有高度非线性术语的多尺度随机部分偏微分方程在强大和弱感中以强大而弱的感觉。
In this paper, we study the strong and weak convergence rates for multi-scale one-dimensional stochastic Burgers equation. Based on the techniques of Galerkin approximation, Kolmogorov equation and Poisson equation, we obtain the slow component strongly and weakly converges to the solution of the corresponding averaged equation with optimal orders 1/2 and 1 respectively. The highly nonlinear term in system brings us huge difficulties, we develop new technique to overcome these difficulties. To the best of our knowledge, this work seems to be the first result in which the optimal convergence orders in strong and weak sense for multi-scale stochastic partial differential equations with highly nonlinear term.
