  In this study, we prove results on the weak solvability and homogenization of
a microscopic semi-linear elliptic system posed in perforated media. The model
presented here explores the interplay between stationary diffusion and both
surface and volume chemical reactions in porous media. Our interest lies in
deriving homogenization limits (upscaling) for alike systems and particularly
in justifying rigorously the obtained averaged descriptions. Essentially, we
prove the well-posedness of the microscopic problem ensuring also the
positivity and boundedness of the involved concentrations and then use the
structure of the two scale expansions to derive corrector estimates
delimitating this way the convergence rate of the asymptotic approximates to
the macroscopic limit concentrations. Our techniques include Moser-like
iteration techniques, a variational formulation, two-scale asymptotic
expansions as well as energy-like estimates.
