Diffusions in perforated domains with mixed boundary conditions
作者:
James P. Dunyak,
期刊:
Stochastic Analysis and Applications
(Taylor Available online 1998)
卷期:
Volume 16,
issue 5
页码: 873-893
ISSN:0736-2994
年代: 1998
DOI:10.1080/07362999808809567
出版商: Marcel Dekker, Inc.
数据来源: Taylor
摘要:
This article investigates averaging effects associated with a fine-grained boundary. A simple diffusion occurs everywhere except at a large number of small “holes” in the medium, at which an appropriately scaled mixed boundary condition is applied. The scaling considered is fitting for boundary conditions resulting from thin layer approximations in which the layer thickness scales with the diameter of the hole. Probabilistic methods associated with the Feynman-Kac formula are applied to find the limiting behavior, and the perforated domain and complex boundary condition are replaced by a straightforward attenuating term.
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