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The present work is aimed to find suitable exchange conditions for saturatedfluid flow in a porous medium, when a fractal microstructure is embedded in theporous matrix. Two different deterministic models are introduced and rigorouslyanalyzed. Also, numerical experiments for each of them are presented to verifythe theoretically predicted behavior of the phenomenon and some probabilisticversions are explored numerically, to gain further insight on the phenomenon.

A Discussion on the Transmission Conditions for Saturated Fluid Flow Through Porous Media With Fractal Microstructure