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Existence of solutions to the equations governing the flow of granular materials. (English) Zbl 0755.76012

Summary: 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. The governing equations reduce to a system of coupled, nonlinear ordinary differential equations with nonlinear 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.

MSC:

76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena
74A99 Generalities, axiomatics, foundations of continuum mechanics of solids
34A34 Nonlinear ordinary differential equations and systems
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