A parabolic cross-diffusion system for granular materials

We analyze a cross-diffusion system of parabolic equations for the relative concentration and the dynamic repose angle of a mixture of two different granular materials in a long rotating drum. The main feature of the system is the ability to describe the axial segregation of the two granular components. The existence of global-in-time weak solutions is shown for arbitrary large cross-diffusion by using entropy-type inequalities and approximation arguments. The uniqueness of solutions is proved if cross-diffusion is not too large. Furthermore, we derive a sufficient condition on the parameters to have nonsegregation. Finally, numerical simulations illustrate the long-time coarsening of the segregation bands in the drum.