ON THE HOMOGENIZATION OF DIFFUSIONS IN PERIODIC COMB-LIKE STRUCTURES
ON THE HOMOGENIZATION OF DIFFUSIONS IN PERIODIC COMB-LIKE STRUCTURES
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关于周期性梳状结构中扩散的均匀化
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
S. Cohn
中科院分区：
文献类型：
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作者：
S. Cohn
在这篇论文中，我们研究了两个特殊梳状结构中扩散的均匀化。在这两个模型中，梳状结构可以看作是一个宏观扩散与捕获机制。该过程花费非平凡的时间在这些陷阱和收敛建立鞅问题和漂移理论。该极限过程具有显式的时变布朗运动的形式，也具有显式的时变布朗运动的形式。限制宏观过程也被证明是一个被困的扩散的Kolmogorov方程有一个长期的分数时间导数。
In this thesis we study the homogenization of diffusions in two particular comb-like structures. In both models, the comb can be viewed as a macroscopic diffusion with a trapping mechanism. The processes spend non-trivial amounts of time in these traps and convergence is established using martingale problems and excursion theory. The limiting process has an explicit form as time-changed Brownian motion and also as the unique solution to a certain system of SDE. The limiting macroscopic process is also shown to be a trapped diffusion whose Kolmogorov equation has a term with fractional-time derivatives.