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This paper treats the solvability of a semilinear reaction-diffusion system,which incorporates transport (diffusion) and reaction effects emerging from twoseparated spatial scales:  $x$ - macro and $y$ - micro. The system's origin connects to the modeling ofconcrete corrosion in sewer concrete pipes. It consists of three partialdifferential equations which are mass-balances of concentrations, as well as,one ordinary differential equation tracking the damage-by-corrosion. The systemis semilinear, partially dissipative, and coupled via the solid-water interfaceat the microstructure (pore) level. The structure of the model equations isobtained in \cite{tasnim1} by upscaling of the physical and chemical processestaking place within the microstructure of the concrete. Herein we ensure thepositivity and $L^\infty-$bounds on concentrations, and then prove theglobal-in-time existence and uniqueness of a suitable class of positive andbounded solutions that are stable with respect to the two-scale data and modelparameters. The main ingredient to prove existence include fixed-pointarguments and convergent two-scale Galerkin approximations.

Distributed space scales in a semilinear reaction-diffusion system including a parabolic variational inequality: A well-posedness study