  We derive an existence result for solutions of a differential system which
characterizes the equilibria of a particular model in granular matter theory,
the so-called partially open table problem for growing sandpiles. Such result
generalizes a recent theorem of Cannarsa and Cardaliaguet 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 sandpiles and we present the results of some simulations.
