  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 \cite{tasnim1} by upscaling of the physical and chemical processes
taking place within the microstructure of the concrete. Herein we ensure the
positivity and $L^\infty-$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.

Analysis of PDEs