HA for Diffusion Problems in Porous Media

In addition to the conventional source term / (at ), we introduce the following micro-sorption term r, (A ) in order to represent microscale adsorption/desorption phenomena in the micro-domain Q.ad  

Considering terms in the series, we have the following relations For terms 0 s )  

That is, the first term of the permrbation is not a function of the micro-domain coordinates X, but the macro-domain coordinates x . 

The result (9.25) is referred to as the microscale equation for the two-scale diffusion problem in porous media. The boundary condition (9.25) is the A -periodic condition (9.17). 

By taking into account the condition (9.17), we introduce a weak form of (9.25) as follows  

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