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In this study, we prove results on the weak solvability and homogenization ofa microscopic semi-linear elliptic system posed in perforated media. The modelpresented here explores the interplay between stationary diffusion and bothsurface and volume chemical reactions in porous media. Our interest lies inderiving homogenization limits (upscaling) for alike systems and particularlyin justifying rigorously the obtained averaged descriptions. Essentially, weprove the well-posedness of the microscopic problem ensuring also thepositivity and boundedness of the involved concentrations and then use thestructure of the two scale expansions to derive corrector estimatesdelimitating this way the convergence rate of the asymptotic approximates tothe macroscopic limit concentrations. Our techniques include Moser-likeiteration techniques, a variational formulation, two-scale asymptoticexpansions as well as energy-like estimates.

Asymptotic analysis of a semi-linear elliptic system in perforated domains: well-posedness and correctors for the homogenization limit