On the uniqueness of a weak solution of the one-dimensional concrete carbonation problem

In our previous works we studied a one-dimensional free-boundary model related to the aggressive penetration of gaseous carbon dioxide in unsaturated concrete. Essentially, global existence and uniqueness of weak solutions to the model were obtained when the initial functions are bounded on the domain. In this paper we investigate the well-posedness of the problem for the case when the initial functions belong to a $L^2$-class. Specifically, the uniqueness of weak solutions is proved by applying the dual equation method.