Analisys of a nonlinear model arising in chemical aggression of marble

We present a simple model describing the chemical aggression undergone by calcium carbonate rocks in presence of acid atmosphere. A large literature is available on the deterioration processes of building stones, in particular in connection with problems concerning historical buildings in the field of Cultural Heritage. It is well known that the greatest aggression is caused by sulfur dioxide and nitrate. In this paper we consider the corrosion caused by sulphur dioxide, which, reacting with calcium carbonate, produces gypsum. The model proposed is obtained by considering both the diffusive and convective effects of propagation and assuming that the porous medium is saturated with a compressible fluid having an assigned polytropic constitutive equation for the pressure. The qualitative behavior of the one dimensional solutions in the fast reaction limit is performed.