We consider a model for the diffusion of N species of isotopes of the same element in a medium, consisting in a parabolic quasilinear system, with Dirichlet boundary condition, in the general hypothesis that the diffusion coefficients possibly are all different. We prove existence and uniqueness of classical solution in the physically relevant assumption that the total concentration of the element is positive and bounded.

The large-time behaviour of the solution of a hyperbolic- parabolic problem in an isolated domain, which models the diffusion of n species of radiative isotopes of the same element, is studied, assuming general hypotheses on the initial data. Depending on the radiative law and on the distribution of the initial concentration, either a uniform distribution for the concentration of each isotope or the presence of oscillations may be possible when t → ∞.