Abstract. In this paper, we introduce a new model for the collapsing
sandpile and we prove existence and uniqueness of a solution for the corresponding
initial value problem. Moreover, we prove the convergence of
the time-stepping approximation of the solution.We use subgradient flows
for variational problems with time dependent gradient constraints. These
gradient constraints are interpreted as the critical angles of the sandpile.
In particular, our model produces an evolution in time of avalanches in a
drying of a sandpile, rather than instantaneous collapse.
http://www.unilim.fr/pages_perso/noureddine.igbida/Articles/gcollapse.pdf