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  established for the totally open table problem.
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