This paper treats the solvability of a semilinear reaction-diffusion system, which incorporates transport (diffusion) and reaction effects emerging from two separated spatial scales: x - macro and y - micro. The system’s origin connects to the modeling of concrete corrosion in sewer concrete pipes. It consists of three partial differential equations which are mass-balances of concentrations, as well as, one ordinary differential equation tracking the damage-by-corrosion. The system is semilinear, partially dissipative, and coupled via the solid-water interface at the microstructure (pore) level. The structure of the model equations is obtained in  by upscaling of the physical and chemical processes taking place within the microstructure of the concrete. Herein we ensure the positivity and L8-bounds on concentrations, and then prove the global-in-time existence and uniqueness of a suitable class of positive and bounded solutions that are stable with respect to the two-scale data and model parameters. The main ingredient to prove existence include fixed-point arguments and convergent two-scale Galerkin approximations.
Keywords: Reaction and diffusion in heterogeneous media, two-scale Galerkin approximations, parabolic variational inequality, well-posedness