Global existence for a 1D parabolic-elliptic model for chemical aggression in permeable materials

We prove global existence and uniqueness of smooth solutions to a nonlinear system of parabolic-elliptic equations, which describes the chemical aggression of a permeable material, like calcium carbonate rocks, in presence of acid atmosphere. This model applies when convective flows are not negligible, due to the high permeability of the material. The global (in time) result is proven by using a weak continuation principle for the local solutions.