  We consider a system of differential equations of Monge-Kantorovich type
which describes the equilibrium configurations of granular material poured by a
constant source on a network. Relying on the definition of viscosity solution
for Hamilton-Jacobi equations on networks, recently introduced by P.-L. Lions
and P. E. Souganidis, we prove existence and uniqueness of the solution of the
system and we discuss its numerical approximation. Some numerical experiments
are carried out.
