Global existence of a solution for a multiscale model describing moisture transport in concrete materials

In the previous study [5] we proved the existence of a solution locally in time for a two-scale problem which is given as a mathematical model for moisture transport arising in a concrete carbonation process. The two-scale model consists of a diffusion equation of the relative humidity in a macro domain and the free boundary problems describing a wetting and drying process in infinite micro domains. In this paper, by improving the diffusion equation of the relative humidity based on the experimental result [3; 10], we construct a globally-in-time solution of the two scale model. For the global existence, we obtain uniform estimates and uniform boundedness of the solution with respect to time and use the method of extending local solutions.