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| 摘要: |
| 本文考虑定义在$\textbf{R}_{+} × [ 0, 1 ]^d$上具有高频振荡随机位势, 带齐次Neumann边界条件的半线性抛物型随机偏微分方程组(SPDEs)的齐次化问题, 其中$d =1,2$或$3$, 利用正则结构理论, 主要结论是方程组的解将依概率收敛到一个确定性抛物型PDEs的解. |
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| Abstract: |
| In this paper, we consider the homogenization problem of semilinear parabolic stochastic partial differential equations ( SPDEs ) with homogeneous Neumann boundary conditions defined on $\textbf{R}_{+} × [ 0, 1 ]^d$ with high-frequency oscillatory random potential, where $d =1,2$ or $ 3 $, by using regularity structures, the main conclusion is that the solution of the system of equations will converge to the solution of a deterministic parabolic PDEs in probability. |
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