AN EXISTENCE RESULT FOR THE SANDPILE PROBLEM ON FLAT TABLES WITH WALLS

We derive an existence result for solutions of a differential system which characterizes the equilibria of a particular modelin granular matter theory, the so-called partially open table problem for growing samples. Such result generalizes a recent theorem of [6] established for the totally open table problem. Here, due to the presence of walls at the boundary, the surface flow density at the equilibrium may result no more continuous nor bounded, and its explicit mathematical characterization is obtained by domain decomposition techniques. At the same time we show how these solutions can be numerically computed as stationary solutions of a dynamical two-layer model for growing sand piles and we present the results of some simulations.