A generalized collapsing sandpile model

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.