Limiting models for equations with large random potential: A review
Limiting models for equations with large random potential: A review
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具有大随机势的方程的限制模型：回顾
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Yu Gu
中科院分区：
文献类型：
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作者：
G. Bal;Yu Gu
本文综述了最近关于具有大的高振荡随机势的椭圆型或抛物型方程解的收敛性的几个结果。根据势函数的相关性，所得到的极限可以是确定性的，也可以是均匀化方程的解，或者是随机的，也可以是随机偏微分方程的解。在前一种情况下，也可以表征非均匀解的剩余随机波动，或者至少确定收敛到确定性极限的速率。我们提出了几个结果，可以通过渐近扰动，图形扩展，概率表示，和多尺度方法的方法。
This paper reviews several results obtained recently in the convergence of solutions to elliptic or parabolic equations with large highly oscillatory random potentials. Depending on the correlation properties of the potential, the resulting limit may be either deterministic and solution of a homogenized equation or random and solution of a stochastic PDE. In the former case, the residual random fluctuations of the heterogeneous solution may also be characterized, or at least the rate of convergence to the deterministic limit established. We present several results that can be obtained by the methods of asymptotic perturbations, diagrammatic expansions, probabilistic representations, and the multiscale method.