A Parabolic Cross-Diffusion System for Granular Materials

Gonzalo Galiano, Ansgar Jüngel, Julián Velasco
2003 SIAM Journal on Mathematical Analysis  
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 is studied. 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 by using entropy-type inequalities and approximation arguments. The uniqueness of solutions is proved if cross-diffusion is not too large.
more » ... Furthermore, we show that in the non-segregating case, the transient solutions converge exponentially fast to the constant steady-state as time tends to infinity. Finally, numerical simulations show the long-time coarsening of the segregation bands in the drum.
doi:10.1137/s0036141002409386 fatcat:dy43igmzbrdudp4lmu4z3q2ln4