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In this paper we consider a drying and wetting process in porous medium to create a mathematical model for concrete carbonation. The process is assumed to be characterized by the growth of the air zone and a diffusion of moisture in the air zone. Under the assumption we proposed a one-dimensional free boundary problem describing adsorption phenomena in a porous medium. The free boundary problem it to find a curve representing the air zone and the relative humidity of the air zone. For the problem we also established existence, uniqueness and a large time behavior of solutions. Here, by improving the method for uniform estimates we can show the existence of a periodic solution of the problem. Also, the extension method is applied in the proof. This idea is quite important and new since the value of the humidity on the free boundary is unknown.

Existence of periodic solution to one dimensional free boundary problems for adsorption phenomena