Existence of solutions to the equations governing the flow of granular materials

In this work, we shall investigate the existence of solutions for the flow of a granular materials down an inclined plane maintained at a constant temperature. The constitutive equation for the stress is one that has been used recently [Rajagopal & Massoudi, 1990]. The governing equations reduce to a system of coupled, non-linear ordinary differential equations with non-linear boundary conditions. We find that these equations admit non-unique solutions, one in which the volume fraction monotonically increases and the other in which it monotonically decreases from the inclined plane to the free surface.

Existence of solutions to the equations governing the flow of granular materials Academic Article