Well-posedness of a moving two-reaction-strips problem modeling chemical corrosion of porous media

We deal with a one-dimensional coupled system of semi-linear reaction-diffusion equations in two a priori unknown moving phases driven by a non-local kinetic condition. The PDEs system models the penetration of gaseous CO2 in unsaturated cement-based porous materials (concrete). The main issue is that CO2 diffusion and fast reaction with Ca(OH)2 in concrete lead to a sudden drop of alkalinity near the steel reinforcement. This effect initiates the chemical corrosion of the material. We address some aspects concerning the existence, uniqueness and stability of local weak solutions. We also present our concept of global solvability of the movingboundary system in question. We illustrate the application of our model to the prediction of carbonation penetration into ordinary Portland concrete samples.